#793

1

8f1d18d464d469f1afcbccc8

Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29

255.2_295.34000000000003

This point is known as the critical temperature. If we name the lines as O-A, A-B, and A-C, the line O-A represents the sublimation line. The line A-B represents the vaporization line, while the line A-C represents the fusion line.

PROPERTIES OF PURE SUBSTANCES

The substances; homogenous in chemical composition.

Ex…

https://www.youtube.com/watch?v=---C9PWC5so

[]

This point is known as the critical temperature. If we name the lines as O-A, A-B, and A-C, the line O-A represents the sublimation line. The line A-B represents the vaporization line, while the line A-C represents the fusion line.

PROPERTIES OF PURE SUBSTANCES

The substances; homogenous in chemical composition.

Ex: H₂O → Water

Saturation temperature → Every liquid boils at a particular temperature corresponding to a particular pressure; that temperature is called saturation temperature.

Triple point → Point where all the three phases of water exist.

[Diagram of phase diagram with points labeled A, B, C, and lines indicating solid, liquid, and vapor phases]

The next is T-S nature of a pure substance where T is temperature and S is entropy. Here is a graph that shows the nature or variation of a pure substance between temperature and entropy plotted at constant pressure. As the temperature increases the entropy increases. But after a certain point, the temperature remains constant while the entropy continues to increase.

T-S nature of pure substances

P = const

And then after that, when entropy increases, temperature also increases. So we get points A, B, C, D, and E. There are several points on this graph and these points are defined as follows: Point A is defined as the subcooled state, which means the initial point. Point B is defined as the saturated liquid state.

T-S nature of pure substances

T
a b c d e
S

That is the point from which the liquid will start changing into vapor. Up to this phase, the substance is in liquid state. Between B to D, it is liquid plus vapor, and after point D, it is totally vapor. So point C is defined as liquid plus vapor state.

T-S nature of pure substances

a → Subcooled state
b → Saturated liquid state

T
↓
b
c d P=const
a
S

319

8

7

1802

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2

bd14e9ef912058b288dd36c5

Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29

416.44_459.84000000000003

Point D is defined as liquid plus vapor state, dry saturated state. While point E is defined as superheat state. Point A is subcool state, that is, the initial state of the liquid changing to vapor. Point B:

T-S nature of pure substances

a → Subcooled state
b → Saturated liquid state
c → Liquid + vapor state
d →
e →…

https://www.youtube.com/watch?v=---C9PWC5so

[]

Point D is defined as liquid plus vapor state, dry saturated state. While point E is defined as superheat state. Point A is subcool state, that is, the initial state of the liquid changing to vapor. Point B:

T-S nature of pure substances

a → Subcooled state
b → Saturated liquid state
c → Liquid + vapor state
d →
e →

P = const

Point C is the saturated liquid state. That is the point from where the liquid will start changing into vapor. Point C is liquid plus vapor state, that is at this phase the liquid and vapor coexist. Point D is dry saturated vapor state, that means the point from which the liquid completely changes into vapor.

T-S nature of pure substances

a → Subcooled state
b → Saturated liquid state
c → Liquid + vapor state
d → Dry saturated vapor state
e → Superheated state

T
P = const

It transforms into vapor at point E, which is the superheated state, or the final state of the vapor. The temperature at B is equal to the temperature at C, which is equal to the temperature at D, and this is known as the saturation temperature. The heat between B and D is known as latent heat.

T-S nature of pure substances

a → Subcooled state
b → Saturated liquid state
c → Liquid + vapor state
d → Dry saturated vapor state
e → Superheated state

T
↓
b c d e P = const
↓ ↓ ↓ ↓
a l+v vapour
S

If you draw the T-S curve for several pressures, that means p1, p2, and p3, we will get a graph like this. At p1, it will be like this; at p2, like this; and at p3, like this. Joining all these points, we will get a dome-like shape.

T-S nature of pure substances

a → Subcooled state
b → Saturated liquid state
c → Liq + vap state
d → dry saturated vapour state
e → Super heat state

Tb = Tc = Td = Tsat

b → d → latent heat

321

8

9

1737

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3

4b7f6e585fd6716cb9e16df3

Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29

540.44_626.4200000000001

This part is known as the saturated vapor line while this part is known as the saturated liquid line. So the saturated vapor line is the locus of all dry saturated vapor states while the saturated liquid line is the locus of all saturated liquid states. The point C, that is the peak point of the dome, is known as the…

https://www.youtube.com/watch?v=---C9PWC5so

[]

This part is known as the saturated vapor line while this part is known as the saturated liquid line. So the saturated vapor line is the locus of all dry saturated vapor states while the saturated liquid line is the locus of all saturated liquid states. The point C, that is the peak point of the dome, is known as the critical point, that is, beyond.

T-S nature of pure substances

Saturated liquid line
P3
P2
P1
Saturated vapor line

At this point, the latent heat will be zero. That means the liquid will directly change into vapor without going into the liquid plus vapor state. This phase is the liquid phase. This phase is the liquid plus vapor phase. While this phase is the fully vapor phase. So, beyond the critical point, the liquid directly changes to vapor without going through the liquid plus vapor phase.

- T-S nature of pure substances
- Saturated vapour line
  - Locus of all dry saturated vapour state
- Saturated liquid line
  - Locus of all saturated liquid state
- C → Critical point

Vapor phase. The next topic is dryness fraction. It is denoted by small x, the amount of dry steam present in the total amount of wet steam. That is, x is equal to zero. X is equal to m v by m l plus m v. Note: The sentence seems to be incomplete or contains a mathematical error. The original transcription has been reproduced as requested.

DRYNESS Fraction

T
L
L+V
V
S

250

6

13

1380

[{"kind":"clip","index":0,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/540.44_626.4200000000001.mp4","text":"This part is known as the saturated vapor line while this part is known as the saturated liquid line. So the saturated vapor line is the locus of all dry saturated vapor states while the saturated liquid line is the locus of all saturated liquid states. The point C, that is the peak point of the dome, is known as the critical point, that is, beyond.","source":"refined_asr"},{"kind":"clip","index":0,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/540.44_626.4200000000001.mp4","text":"T-S nature of pure substances\n\nSaturated liquid line\nP3\nP2\nP1\nSaturated vapor line","source":"ocr_qwen2_vl_72b"},{"kind":"clip","index":1,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/626.4200000000001_656.38.mp4","text":"At this point, the latent heat will be zero. That means the liquid will directly change into vapor without going into the liquid plus vapor state. This phase is the liquid phase. This phase is the liquid plus vapor phase. While this phase is the fully vapor phase. So, beyond the critical point, the liquid directly changes to vapor without going through the liquid plus vapor phase.","source":"refined_asr"},{"kind":"clip","index":1,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/626.4200000000001_656.38.mp4","text":"- T-S nature of pure substances\n- Saturated vapour line\n  - Locus of all dry saturated vapour state\n- Saturated liquid line\n  - Locus of all saturated liquid state\n- C → Critical point","source":"ocr_qwen2_vl_72b"},{"kind":"clip","index":2,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/656.38_708.72.mp4","text":"Vapor phase. The next topic is dryness fraction. It is denoted by small x, the amount of dry steam present in the total amount of wet steam. That is, x is equal to zero. X is equal to m v by m l plus m v. Note: The sentence seems to be incomplete or contains a mathematical error. The original transcription has been reproduced as requested.","source":"refined_asr"},{"kind":"clip","index":2,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/656.38_708.72.mp4","text":"DRYNESS Fraction\n\nT\nL\nL+V\nV\nS","source":"ocr_qwen2_vl_72b"}]

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4

b91b68d4e343110a2a39d8f1

Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29

708.72_753.1

Where m is the mass of dry vapor, m_l is the mass of liquid or wet vapor. Clearly, with this definition, you may have understood that x, or the dryness fraction, can only be defined within this zone - that is, inside this dome. This dome is known as the vapor-liquid dome because inside this dome, both the liquid and t…

https://www.youtube.com/watch?v=---C9PWC5so

[]

Where m is the mass of dry vapor, m_l is the mass of liquid or wet vapor. Clearly, with this definition, you may have understood that x, or the dryness fraction, can only be defined within this zone - that is, inside this dome. This dome is known as the vapor-liquid dome because inside this dome, both the liquid and the vapor phases coexist.

DRYNESS Fraction

Denoted by 'x'

⇒ amount of dry steam present in total amount of wet steam

i.e., x = mv → ma
mL + mv

Phase exists. So at the starting point, it is all liquid. That means the X value is zero because there is no dry vapor present; the mass of the vapor is zero. And at the right side, all the substance is converted into vapor. That means X is equal to one; it's all vapor.

DRYNESS FRACTION

T

L + V
V

mass of dry steam present
amount of wet steam
→ mass of dry vapour
mass of dry / wet vapour

If the mass of the liquid is totally equal to the liquid, the liquid mass will be zero. Therefore, the vapor mass is the total mass of the steam. So, X is equal to one. Between these points, where X is equal to zero and X is equal to one, the dryness fraction varies inside this dome.

DRYNESS Fraction

Denoted by 'x'

⇒ amount of dry steam present
in total amount of wet steam

i.e., x = m_v / (m_l + m_v)
mass of dry vapour
mass of dry/wet vapour

Now consider the T-S diagram once again. Here we will know some important relations while calculating the dryness fraction. The endpoint on the right-hand side of the dome is represented by X-if, while the left-hand side is represented by G. So, between these two, entropy is represented.

- Dryness Fraction

  - Denoted by 'x'
  - Amount of dry steam present in total amount of wet steam
  - \( x = \frac{m_v}{m_l + m_v} \)
    - \( m_v \): mass of dry vapour
    - \( m_l + m_v \): mass of dry/wet vapour

- Graphs:
  - Left graph: Temperature (T) vs. Entropy (S)
  - Right graph: Temperature (T) vs. Entropy (S) with a peak and a horizontal line indicating a phase change.

By SFG which is equal to SF minus SG Similarly if on the X-axis we have enthalpy then HFG that will be equal to HF minus HG Similarly for volume VFG will be equal to VF minus VG If we need to find out the value of entropy or enthalpy between or inside this zone we

- Dryness Fraction
- Denoted by 'x'
- amount of dry steam present in total amount of wet steam
- x = mv / (mv + mL)
- mass of dry vapour
- mass of dry/wet vapour

- T-S diagram
- g: gas
- f: fluid
- sfg: specific heat of vaporization

472

10

8

2489

[{"kind":"clip","index":0,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/708.72_753.1.mp4","text":"Where m is the mass of dry vapor, m_l is the mass of liquid or wet vapor. Clearly, with this definition, you may have understood that x, or the dryness fraction, can only be defined within this zone - that is, inside this dome. This dome is known as the vapor-liquid dome because inside this dome, both the liquid and the vapor phases coexist.","source":"refined_asr"},{"kind":"clip","index":0,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/708.72_753.1.mp4","text":"DRYNESS Fraction\n\nDenoted by 'x'\n\n⇒ amount of dry steam present in total amount of wet steam\n\ni.e., x = mv → ma\nmL + mv","source":"ocr_qwen2_vl_72b"},{"kind":"clip","index":1,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/753.1_777.5600000000001.mp4","text":"Phase exists. So at the starting point, it is all liquid. That means the X value is zero because there is no dry vapor present; the mass of the vapor is zero. And at the right side, all the substance is converted into vapor. That means X is equal to one; it's all vapor.","source":"refined_asr"},{"kind":"clip","index":1,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/753.1_777.5600000000001.mp4","text":"DRYNESS FRACTION\n\nT\n\nL + V\nV\n\nmass of dry steam present\namount of wet steam\n→ mass of dry vapour\nmass of dry / wet vapour","source":"ocr_qwen2_vl_72b"},{"kind":"clip","index":2,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/777.5600000000001_796.58.mp4","text":"If the mass of the liquid is totally equal to the liquid, the liquid mass will be zero. Therefore, the vapor mass is the total mass of the steam. So, X is equal to one. Between these points, where X is equal to zero and X is equal to one, the dryness fraction varies inside this dome.","source":"refined_asr"},{"kind":"clip","index":2,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/777.5600000000001_796.58.mp4","text":"DRYNESS Fraction\n\nDenoted by 'x'\n\n⇒ amount of dry steam present\nin total amount of wet steam\n\ni.e., x = m_v / (m_l + m_v)\nmass of dry vapour\nmass of dry/wet vapour","source":"ocr_qwen2_vl_72b"},{"kind":"clip","index":3,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/796.58_826.58.mp4","text":"Now consider the T-S diagram once again. Here we will know some important relations while calculating the dryness fraction. The endpoint on the right-hand side of the dome is represented by X-if, while the left-hand side is represented by G. So, between these two, entropy is represented.","source":"refined_asr"},{"kind":"clip","index":3,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/yout

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[{"image_index":0,"interleaved_index":0,"member_name":"dataset_images_interval_7/---C9PWC5so/[email protected]_753.1#1.jpg","source_image_path":"/mnt/workspace/zwq_data/interleaved_dataset/dataset_images_interval_7/---C9PWC5so/[email protected]_753.1#1.jpg","caption":"We can see these text from the image: DRYNESS Fraction\n\nDenoted by 'x'\n\n⇒ amount of dry steam present in total amount of wet steam\n\ni.e., x = mv → ma\nmL + mv.\n Where m is the mass of dry vapor, m_l is the mass of liquid or wet vapor. Clearly, with this definition, you may have understood that x, or the dryness fraction, can only be defined within this zone - that is, inside this dome. This dome is known as the vapor-liquid dome because inside this dome, both the liquid and the vapor phases coexist.","caption_source":"text_ocr","caption_distance":2,"image_byte_len":30448,"image_sha256":"6b01fd46a7bd82ff6e75558eb1d485e89b634205979b93c950caaadc3dd931a2","image_width":1280,"image_height":720,"token_estimate":3600,"dhash":"0f0f8f0f0f0f0d27","vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/708.72_753.1.mp4","source_record_index":375110,"sample_id":"b91b68d4e343110a2a39d8f1","crop":{"source_record_index":375110,"frame_index":0,"frame_available":true,"orig_width":1280,"orig_height":720,"crop_status":"accepted","crop_box_x":72,"crop_box_y":0,"crop_box_w":1208,"crop_box_h":720,"crop_confidence":0.6616776733437463,"crop_candidate":"ocr_tight:boxes=13","crop_candidate_count":4,"crop_text_mass":1.0,"crop_visual_text_mass":0.997258911145821,"crop_ocr_box_recall":1.0,"crop_ocr_area_recall":1.0,"crop_ocr_cut_count":0.0,"crop_ocr_box_count":13.0,"crop_ocr_status":"ok:easyocr:13","crop_relevance":0.9686294555729105,"crop_reason":"accepted: mode=content confidence=0.662 area_ratio=0.944 score_mass=0.997 text_mass=1.000 visual_text_mass=0.997 ocr_box_recall=1.000 ocr_area_recall=1.000 ocr_cuts=0 ocr_status=ok:easyocr:13 relevance=0.969 x_mass=0.914 y_mass=0.911 candidate=ocr_tight:boxes=13 context=0.40:gesture_terms","crop_preview_rel":"","orig_preview_rel":"","failure_flags":[]}},{"image_index":1,"interleaved_index":1,"member_name":"dataset_images_interval_7/---C9PWC5so/[email protected]_753.1#6.jpg","source_image_path":"/mnt/workspace/zwq_data/interleaved_dataset/dataset_images_interval_7/---C9PWC5so/[email protected]_753.1#6.jpg","caption":"We can see these text from the image: DRYNESS Fraction\n\nDenoted by 'x'\n\n⇒ amount of dry steam present in total amount of wet steam\n\ni.e., x = mv → ma\nmL + mv.\n Where m is the mass of dry vapor, m_l is the mass of liquid or wet vapor. Clearly, with this definition, you may have understood that x, or the dryness fraction, can only be defined within this zone - that is, inside this dome. This dome is known as the vapor-liquid dome because inside this dome, both the liquid and the vapor phases coexist.","caption_source":"text_ocr","caption_distance":1,"image_byte_len":48403,"image_sha256":"f143cac0f23a16133eec62b2f0e51f57fdb89d925e028800c9ffd7a81fb9d77b","image_width":1280,"image_height":720,"token_estimate":3600,"dhash":"0f0f8f0f27672537","vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/708.72_753.1.mp4","source_record_index":375110,"sample_id":"b91b68d4e343110a2a39d8f1","crop":{"source_record_index":375110,"frame_index":1,"frame_available":true,"orig_width":1280,"orig_height":720,"crop_status":"accepted","crop_box_x":76,"crop_box_y":0,"crop_box_w":1204,"crop_box_h":720,"crop_confidence":0.6629547628113539,"crop_candidate":"ocr_tight:boxes=6","crop_candidate_count":4,"crop_text_mass":1.0,"crop_visual_text_mass":0.9973492093711801,"crop_ocr_box_reca

5

8e3ef9c92666c7347e312281

Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29

99.84_129.14000000000001

For every liquid, a liquid boils at a particular temperature for a given corresponding pressure. That temperature is called the saturation temperature, and the pressure at which it is boiling is known as the saturation pressure. As I told,

Properties Of Pure Substances

The substances; homogenous in chemical composit…

https://www.youtube.com/watch?v=---C9PWC5so

[]

For every liquid, a liquid boils at a particular temperature for a given corresponding pressure. That temperature is called the saturation temperature, and the pressure at which it is boiling is known as the saturation pressure. As I told,

Properties Of Pure Substances

The substances; homogenous in chemical composition.

Ex: H2O -> Water

Saturation temperature -> Every liquid boils at a particular temperature corresponding to a particular pressure; that temperature is called saturation temperature.

Above that water, which means H2O, is an example of a pure substance. So let's try to study the nature or the variation of pressure with respect to the temperature of water. This graph shows the variation of pressure with the temperature of water. This line is known as the sublimation line, while this line is known as the vaporization line, and

- Properties Of Pure Substances
- The substances; homogenous in chemical composition.
- Ex: H₂O → Water
- Saturation temperature → Every liquid boils at a particular temperature corresponding to a particular pressure; that temperature is called saturation temperature.

This line is known as the fusion line. Between the sublimation line and the fusion line, the solid state exists. And between the sublimation line and the vaporization line, the vapor phase exists. And between the fusion line and the vaporization line, the liquid phase of water exists.

- Properties Of Pure Substances
- The substances; homogenous in chemical composition.
- Ex: H₂O => Water
- Saturation temperature -> Every liquid boils at a particular temperature corresponding to a particular pressure; that temperature is called saturation temperature.
- Diagram: P (pressure) vs. T (temperature) with phases labeled as Solid, Liquid, and Vapour.

Now in this graph, you can see there is an intersection of three lines coming at one point. This intersection point has a temperature; this is known as the critical temperature, and this point is known as the triple point. Hence, the triple point is defined as the point where all three phases of water coexist in equilibrium.

- Properties Of Pure Substances

- The substances; homogenous in chemical composition.

- Example: H₂O → Water

- Saturation temperature → Every liquid boils at a particular temperature corresponding to a particular pressure; that temperature is called saturation temperature.

A pure substance exists. Now in this graph, you can see there is an intersection of three lines at one point. Here you can see that at this point, the liquid phase exists, the vapor phase exists, as well as the solid phase. That is why it is known as the triple point. And the temperature corresponding to the triple point.

- Properties of Pure Substances
- The substances; homogenous in chemical composition.
- Example: H₂O → Water
- Saturation temperature → Every liquid boils at a particular temperature corresponding to a particular pressure; that temperature is called saturation temperature.
- Triple point → Point where all the three phases of water exist.
- Diagram: Liquid, Solid, Vapour

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[{"kind":"clip","index":0,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/99.84_129.14000000000001.mp4","text":"For every liquid, a liquid boils at a particular temperature for a given corresponding pressure. That temperature is called the saturation temperature, and the pressure at which it is boiling is known as the saturation pressure. As I told,","source":"refined_asr"},{"kind":"clip","index":0,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/99.84_129.14000000000001.mp4","text":"Properties Of Pure Substances\n\nThe substances; homogenous in chemical composition.\n\nEx: H2O -> Water\n\nSaturation temperature -> Every liquid boils at a particular temperature corresponding to a particular pressure; that temperature is called saturation temperature.","source":"ocr_qwen2_vl_72b"},{"kind":"clip","index":1,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/129.14000000000001_165.28.mp4","text":"Above that water, which means H2O, is an example of a pure substance. So let's try to study the nature or the variation of pressure with respect to the temperature of water. This graph shows the variation of pressure with the temperature of water. This line is known as the sublimation line, while this line is known as the vaporization line, and","source":"refined_asr"},{"kind":"clip","index":1,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/129.14000000000001_165.28.mp4","text":"- Properties Of Pure Substances\n- The substances; homogenous in chemical composition.\n- Ex: H₂O → Water\n- Saturation temperature → Every liquid boils at a particular temperature corresponding to a particular pressure; that temperature is called saturation temperature.","source":"ocr_qwen2_vl_72b"},{"kind":"clip","index":2,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/165.28_192.08.mp4","text":"This line is known as the fusion line. Between the sublimation line and the fusion line, the solid state exists. And between the sublimation line and the vaporization line, the vapor phase exists. And between the fusion line and the vaporization line, the liquid phase of water exists.","source":"refined_asr"},{"kind":"clip","index":2,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/165.28_192.08.mp4","text":"- Properties Of Pure Substances\n- The substances; homogenous in chemical composition.\n- Ex: H₂O => Water\n- Saturation temperature -> Every liquid boils at a particular temperature corresponding to a particular pressure; that temperature is called saturation temperature.\n- Diagram: P (pressure) vs. T (temperature) with phases labeled as Solid, Liquid, and Vapour.","source":"ocr_qwen2_vl_72b"},{"kind":"clip","index":3,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingA

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6

7160f8632fe53992a19e2a8b

Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29

868.12_897.12

Use the relation. For entropy, it will be: Sx is equal to SG plus X times SFG. For enthalpy, it will be: HX is equal to HG plus X times HFG. The values of SFG, HFG will be calculated through the steam table.

- Dryness Fraction
- Denoted by 'x'
- amount of dry steam present in total amount of wet steam
- i.e., \( x =…

https://www.youtube.com/watch?v=---C9PWC5so

[]

Use the relation. For entropy, it will be: Sx is equal to SG plus X times SFG. For enthalpy, it will be: HX is equal to HG plus X times HFG. The values of SFG, HFG will be calculated through the steam table.

- Dryness Fraction
- Denoted by 'x'
- amount of dry steam present in total amount of wet steam
- i.e., \( x = \frac{m_v}{m_l + m_v} \)
- mass of dry vapour
- mass of dry/wet vapour

- \( S_{fg} = S_f - S_g \)
- \( h_{fg} = h_f - h_g \)
- \( v_{fg} = v_f - v_g \)

The next is PV nature of the pure substance, that is, pressure-volume nature. So far, we learned PT and the TS nature of the pure substance. Now, the PV nature of the pure substance. Here, the dome is shifting more towards the right side and it's drawn at constant temperature. Notice the difference.

P-V nature

T = const.

x = 0
x = 1

Temperature pressure is decreasing in nature. That means it is coming from up to down. And the shape of the dome is slightly changed. On the left-hand side, it's quite similar. While on the right-hand side, it is more shifting towards the right side. This is the nature of the pressure-volume curve of the pure substance.

- P-V nature
- T = Const
- x = 0
- x = 1

Let's move on to the h-s curve which stands for enthalpy versus entropy curve This is also known as Mollier's chart The dome you see here has a distinct shape It's plotted along constant temperature lines which are indicated here And constant pressure lines which are shown here Now let's discuss dryness fraction

The dryness fraction changes from here, X equals to 0, to X equals to 1. For example, in this diagram, it has shown the dryness fraction line is changing from here in the mix. At the line of X equals to 0.8, it is shown X equals to 0.9. Now, this diagram is very important to find.

- 1000 bar
- 310°C
- 220°C
- Line of constant temperature
- Ts
- T4
- T3
- T2
- T1
- Saturation line
- Ps
- P5
- P4
- P3
- P2
- P1
- Lines of constant pressure
- P = 10 bar
- P = 5 bar
- P = 1 bar
- P = 0.1 bar
- P = 0.01 bar
- x = 0.9
- x = 0.8
- x = 0.7
- x = 0.6
- x = 0.5
- x = 0.4
- x = 0.3
- x = 0.2
- x = 0.1
- Critical point
- 2000
- Enthalpy, h (kJ/kg)
- Entropy, s (kJ/kg K)

Let's find the value of enthalpy or the entropy for a specific given temperature and pressure. Suppose the temperature is given, let's consider 220 degrees Celsius and the pressure is given as 5 bar. So, considering the 5 bar line and the 220-degree Celsius line.

- Critical point
- 2000
- Entropy, s kJ/kg K
- Enthalpy, h kJ/kg
- Line of constant temperature
- Saturation line
- T1
- T2
- T3
- T4
- T5
- P1
- P2
- P3
- P4
- P5
- P6
- P7
- P8
- P9
- P10
- P11
- P12
- P13
- P14
- P15
- P16
- P17
- P18
- P19
- P20
- P21
- P22
- P23
- P24
- P25
- P26
- P27
- P28
- P29
- P30
- P31
- P32
- P33
- P34
- P35
- P36
- P37
- P38
- P39
- P40
- P41
- P42
- P43
- P44
- P45
- P46
- P47
- P48
- P49
- P50
- P51
- P52
- P53
- P54
- P55
- P56
- P57
- P58
- P59
- P60
- P61
- P62
- P63
- P64
- P65
- P66
- P67
- P68
- P69
- P70
- P71
- P72
- P73
- P74
- P75
- P76
- P77
- P78
- P79
- P80
- P81
- P82
- P83
- P84
- P85
- P86
- P87
- P88
- P89
- P90
- P91
- P92
- P93
- P94
- P95
- P96
- P97
- P98
- P99
- P100
- 220°C
- 310°C

604

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7

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[{"kind":"clip","index":0,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/868.12_897.12.mp4","text":"Use the relation. For entropy, it will be: Sx is equal to SG plus X times SFG. For enthalpy, it will be: HX is equal to HG plus X times HFG. The values of SFG, HFG will be calculated through the steam table.","source":"refined_asr"},{"kind":"clip","index":0,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/868.12_897.12.mp4","text":"- Dryness Fraction\n- Denoted by 'x'\n- amount of dry steam present in total amount of wet steam\n- i.e., \\( x = \\frac{m_v}{m_l + m_v} \\)\n- mass of dry vapour\n- mass of dry/wet vapour\n\n- \\( S_{fg} = S_f - S_g \\)\n- \\( h_{fg} = h_f - h_g \\)\n- \\( v_{fg} = v_f - v_g \\)","source":"ocr_qwen2_vl_72b"},{"kind":"clip","index":1,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/897.12_925.08.mp4","text":"The next is PV nature of the pure substance, that is, pressure-volume nature. So far, we learned PT and the TS nature of the pure substance. Now, the PV nature of the pure substance. Here, the dome is shifting more towards the right side and it's drawn at constant temperature. Notice the difference.","source":"refined_asr"},{"kind":"clip","index":1,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/897.12_925.08.mp4","text":"P-V nature\n\nT = const.\n\nx = 0\nx = 1","source":"ocr_qwen2_vl_72b"},{"kind":"clip","index":2,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/925.08_948.52.mp4","text":"Temperature pressure is decreasing in nature. That means it is coming from up to down. And the shape of the dome is slightly changed. On the left-hand side, it's quite similar. While on the right-hand side, it is more shifting towards the right side. This is the nature of the pressure-volume curve of the pure substance.","source":"refined_asr"},{"kind":"clip","index":2,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/925.08_948.52.mp4","text":"- P-V nature\n- T = Const\n- x = 0\n- x = 1","source":"ocr_qwen2_vl_72b"},{"kind":"clip","index":3,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio#####doingASR#####FinishASR/---C9PWC5so/948.52_977.5400000000001.mp4","text":"Let's move on to the h-s curve which stands for enthalpy versus entropy curve This is also known as Mollier's chart The dome you see here has a distinct shape It's plotted along constant temperature lines which are indicated here And constant pressure lines which are shown here Now let's discuss dryness fraction","source":"refined_asr"},{"kind":"clip","index":3,"vid":"---C9PWC5so.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Mechanical Engineering Thermodynamics: Fundamentals of Properties of Pure Substances Tutorial_29.json#####audio##

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7

92e2b78387726a9be0b28da7

Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30

109.16_129.48

This is known as the hydraulic gradient, which is denoted by the symbol I. So in place of HL upon L, we can replace this by I times A. Now, if we remove this proportionality sign, we get a constant value, that is, K times I times A.

Darcy’s Law for determining Ground Water Velocity

On the- basis of experimental evid…

https://www.youtube.com/watch?v=---DC2PP_TI

[]

This is known as the hydraulic gradient, which is denoted by the symbol I. So in place of HL upon L, we can replace this by I times A. Now, if we remove this proportionality sign, we get a constant value, that is, K times I times A.

Darcy’s Law for determining Ground Water Velocity

On the- basis of experimental evidence, Mr H. Darcy, a French Scientist enunciated in 1865, a law governing the rate of flow (i.e. the discharge) through soils. According to him, this discharge was directly proportional to the head loss (HL), and the area of cross-section(A) of the soil, and inversely proportional to the length of the soil sample (L).

In other words,

Q ∝ HL . A

But represents the rate of loss of head, i.e. the hydraulic gradient

where, K is the proportionality constant and was found to be changing with the type of soil, and hence represented a property of the soil, called permeability or coefficient of permeability.

The above equation becomes dimensionally compatible, if K has the units of L/T, i.e. say cm/sec, i.e. the units of velocity.

The Darcy’s law has been demonstrated to be valid only for laminar flow conditions, which as far as soils are concerned, is not at all a serious problem, because the flow in sands, silts and clays is invariably laminar.

Now this is the formulation given by Darcy where K is a proportionality constant. When we experimented and the data was collected regarding the different types of soil it was found to be changing with the type of soil and therefore it was represented as the property of the soil.

Darcy’s Law for determining Ground Water Velocity

On the basis of experimental evidence, Mr H. Darcy, a French Scientist enunciated in 1865, a law governing the rate of flow (i.e., the discharge) through soils. According to him, this discharge was directly proportional to the head loss (HL), and the area of cross-section (A) of the soil, and inversely proportional to the length of the soil sample (L).

In other words,

\[ Q \propto \frac{H_L}{L} \cdot A \]

But \(\frac{H_L}{L}\) represents the rate of loss of head, i.e., the hydraulic gradient (\(i\)).

\[ Q \propto i \cdot A \]

\[ Q = k \cdot i \cdot A \]

where, K is the proportionality constant and was found to be changing with the type of soil, and hence represented a property of the soil, called permeability or coefficient of permeability.

The above equation becomes dimensionally compatible, if K has the units of L/T, i.e., say cm/sec, i.e., the units of velocity.

The Darcy’s law has been demonstrated to be valid only for laminar flow conditions, which as far as soils are concerned, is not at all a serious problem, because the flow in sands, silts and clays is invariably laminar.

And that property is known as the permeability or the coefficient of permeability. Now this equation becomes dimensional. It is not necessarily dimensionally compatible because we know this: Q is the rate of flow, that is, cubic meter per second. For the K, we do not know the units.

Darcy’s Law for determining Ground Water Velocity

On the- basis of experimental evidence, Mr H. Darcy, a French Scientist enunciated in 1865, a law governing the rate of flow (i.e. the discharge) through soils. According to him, this discharge was directly proportional to the head loss (HL), and the area of cross-section(A) of the soil, and inversely proportional to the length of the soil sample (L).

In other words,

Q ∝ HL . A
L

But represents the rate of loss of head, i.e. the hydraulic gradient (i)

Q ∝ i . A
⇒ Q = k i A

where, K is the proportionality constant and was found to be changing with the type of soil, and hence represented a property of the soil, called permeability or coefficient of permeability.

The above equation becomes dimensionally compatible; if K has the units of L/T, i.e. say cm/sec, i.e. the units of velocity.

The Darcy’s law has been demonstrated to be valid only for laminar flow conditions, which as far as soils are concerned, is not at all a serious p

1443

12

1

8011

[{"kind":"clip","index":0,"vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30.json#####audio#####doingASR#####FinishASR/---DC2PP_TI/109.16_129.48.mp4","text":"This is known as the hydraulic gradient, which is denoted by the symbol I. So in place of HL upon L, we can replace this by I times A. Now, if we remove this proportionality sign, we get a constant value, that is, K times I times A.","source":"refined_asr"},{"kind":"clip","index":0,"vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30.json#####audio#####doingASR#####FinishASR/---DC2PP_TI/109.16_129.48.mp4","text":"Darcy’s Law for determining Ground Water Velocity\n\nOn the- basis of experimental evidence, Mr H. Darcy, a French Scientist enunciated in 1865, a law governing the rate of flow (i.e. the discharge) through soils. According to him, this discharge was directly proportional to the head loss (HL), and the area of cross-section(A) of the soil, and inversely proportional to the length of the soil sample (L).\n\nIn other words,\n\nQ ∝ HL . A\n\nBut represents the rate of loss of head, i.e. the hydraulic gradient\n\nwhere, K is the proportionality constant and was found to be changing with the type of soil, and hence represented a property of the soil, called permeability or coefficient of permeability.\n\nThe above equation becomes dimensionally compatible, if K has the units of L/T, i.e. say cm/sec, i.e. the units of velocity.\n\nThe Darcy’s law has been demonstrated to be valid only for laminar flow conditions, which as far as soils are concerned, is not at all a serious problem, because the flow in sands, silts and clays is invariably laminar.","source":"ocr_qwen2_vl_72b"},{"kind":"clip","index":1,"vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30.json#####audio#####doingASR#####FinishASR/---DC2PP_TI/129.48_153.8.mp4","text":"Now this is the formulation given by Darcy where K is a proportionality constant. When we experimented and the data was collected regarding the different types of soil it was found to be changing with the type of soil and therefore it was represented as the property of the soil.","source":"refined_asr"},{"kind":"clip","index":1,"vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30.json#####audio#####doingASR#####FinishASR/---DC2PP_TI/129.48_153.8.mp4","text":"Darcy’s Law for determining Ground Water Velocity\n\nOn the basis of experimental evidence, Mr H. Darcy, a French Scientist enunciated in 1865, a law governing the rate of flow (i.e., the discharge) through soils. According to him, this discharge was directly proportional to the head loss (HL), and the area of cross-section (A) of the soil, and inversely proportional to the length of the soil sample (L).\n\nIn other words,\n\n\\[ Q \\propto \\frac{H_L}{L} \\cdot A \\]\n\nBut \\(\\frac{H_L}{L}\\) represents the rate of loss of head, i.e., the hydraulic gradient (\\(i\\)).\n\n\\[ Q \\propto i \\cdot A \\]\n\n\\[ Q = k \\cdot i \\cdot A \\]\n\nwhere, K is the proportionality constant and was found to be changing with the type of soil, and hence represented a property of the soil, called permeability or coefficient of permeability.\n\nThe above equation becomes dimensionally compatible, if K has the units of L/T, i.e., say cm/sec, i.e., the units of velocity.\n\nThe Darcy’s law has been demonstrated to be valid only for laminar flow conditions, which as far as soils are concerned, is not at all a serious problem, because the flow in sands, silts and clays is invariably laminar.","source":"ocr_qwen2_vl_72b"},{"kind":"clip","index":2,"vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/yo

[
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8

4e816eaa58fa8ea4ac3465fa

Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30

247.6_276.96

It's equal to K. If we divide both sides of the equation by the area, it becomes Q over A is equal to K times IA over A. So this A cancels out. From here, this Q over A, which is discharge over area, is known as velocity V, and it's equal to K times I.

Dividing both sides of equation by A, we get

where v is the disc…

https://www.youtube.com/watch?v=---DC2PP_TI

[]

It's equal to K. If we divide both sides of the equation by the area, it becomes Q over A is equal to K times IA over A. So this A cancels out. From here, this Q over A, which is discharge over area, is known as velocity V, and it's equal to K times I.

Dividing both sides of equation by A, we get

where v is the discharge velocity, and is not the actual flow velocity through the soil medium, since the flow occurs through the voids of cross-sectional area A, and not in A itself. The permeability of the soil can then be viewed as this superficial velocity under a unit hydraulic gradient.

If A is the area of the voids, then

where Va is the actual velocity of flow of water through the soil. Then

when A is large in comparison, we can safely assume that the ratio of the area of the void(Av) to the total area (A) is the same as the ratio of the volume of the voids (Vv)to the total volume (V), i.e. equal to porosity (n).

Hence,

Now, where V is the discharge velocity, it is not the actual flow velocity through the soil medium. The difference between this discharge velocity and the actual flow velocity is that this discharge is taking place through the voids of the cross-sectional area and not the total area itself. Because of this, this is considered to be the

Dividing both sides of equation by A, we get

\[
\frac{Q}{A} = \frac{k i A}{A} \Rightarrow v = k i
\]

where \( v \) is the discharge velocity, and is not the actual flow velocity through the soil medium, since the flow occurs through the voids of cross-sectional area \( A \), and not in \( A \) itself. The permeability of the soil can then be viewed as this superficial velocity under a unit hydraulic gradient.

If \( A \) is the area of the voids, then

where \( V_a \) is the actual velocity of flow of water through the soil. Then

when \( A \) is large in comparison, we can safely assume that the ratio of the area of the void (\( A_v \)) to the total area (\( A \)) is the same as the ratio of the volume of the voids (\( V_v \)) to the total volume (\( V \)), i.e., equal to porosity (\( n \)).

Hence,

Let's consider the velocity. If we take the area of voids as A_V, then the area of voids multiplied by the actual velocity through the voids equals the total area times the superficial velocity. Here, V_EA represents the actual velocity of the flow.

Dividing both sides of equation by A, we get

\[ \frac{Q}{A} = \frac{k i A}{A} \Rightarrow v = k i \]

where \( v \) is the discharge velocity, and is not the actual flow velocity through the soil medium, since the flow occurs through the voids of cross-sectional area \( A \), and not in \( A \) itself. The permeability of the soil can then be viewed as this superficial velocity under a unit hydraulic gradient.

If \( A_v \) is the area of the voids, then

where \( V_a \) is the actual velocity of flow of water through the soil. Then

when \( A \) is large in comparison, we can safely assume that the ratio of the area of the void (\( A_v \)) to the total area (\( A \)) is the same as the ratio of the volume of the voids (\( V_v \)) to the total volume (\( V \)), i.e., equal to porosity (\( n \)).

Hence,

Through the soil, then VEA will be calculated as VA into AV upon A. Now if the area of the medium is large in comparison to the area of the voids, we can safely assume that this ratio of AV upon A, that is same as volume of voids to the total volume, and this is nothing but the porosity. The sentence appears to be technical in nature and is grammatically correct with no repetitions or obvious errors. However without context it's hard to ensure complete accuracy. If this is a scientific or technical text it may benefit from being reviewed by someone with expertise in the relevant field.

Dividing both sides of equation by A, we get

\[
\frac{Q}{A} = \frac{k i A}{A} \Rightarrow v = k i
\]

where \(v\) is the discharge velocity, and is not the actual flow velocity through the soil medium, since the flow occurs through the voids o

1089

10

4

5768

[{"kind":"clip","index":0,"vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30.json#####audio#####doingASR#####FinishASR/---DC2PP_TI/247.6_276.96.mp4","text":"It's equal to K. If we divide both sides of the equation by the area, it becomes Q over A is equal to K times IA over A. So this A cancels out. From here, this Q over A, which is discharge over area, is known as velocity V, and it's equal to K times I.","source":"refined_asr"},{"kind":"clip","index":0,"vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30.json#####audio#####doingASR#####FinishASR/---DC2PP_TI/247.6_276.96.mp4","text":"Dividing both sides of equation by A, we get\n\nwhere v is the discharge velocity, and is not the actual flow velocity through the soil medium, since the flow occurs through the voids of cross-sectional area A, and not in A itself. The permeability of the soil can then be viewed as this superficial velocity under a unit hydraulic gradient.\n\nIf A is the area of the voids, then\n\nwhere Va is the actual velocity of flow of water through the soil. Then\n\nwhen A is large in comparison, we can safely assume that the ratio of the area of the void(Av) to the total area (A) is the same as the ratio of the volume of the voids (Vv)to the total volume (V), i.e. equal to porosity (n).\n\nHence,","source":"ocr_qwen2_vl_72b"},{"kind":"clip","index":1,"vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30.json#####audio#####doingASR#####FinishASR/---DC2PP_TI/278.08000000000004_307.20000000000005.mp4","text":"Now, where V is the discharge velocity, it is not the actual flow velocity through the soil medium. The difference between this discharge velocity and the actual flow velocity is that this discharge is taking place through the voids of the cross-sectional area and not the total area itself. Because of this, this is considered to be the","source":"refined_asr"},{"kind":"clip","index":1,"vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30.json#####audio#####doingASR#####FinishASR/---DC2PP_TI/278.08000000000004_307.20000000000005.mp4","text":"Dividing both sides of equation by A, we get\n\n\\[\n\\frac{Q}{A} = \\frac{k i A}{A} \\Rightarrow v = k i\n\\]\n\nwhere \\( v \\) is the discharge velocity, and is not the actual flow velocity through the soil medium, since the flow occurs through the voids of cross-sectional area \\( A \\), and not in \\( A \\) itself. The permeability of the soil can then be viewed as this superficial velocity under a unit hydraulic gradient.\n\nIf \\( A \\) is the area of the voids, then\n\nwhere \\( V_a \\) is the actual velocity of flow of water through the soil. Then\n\nwhen \\( A \\) is large in comparison, we can safely assume that the ratio of the area of the void (\\( A_v \\)) to the total area (\\( A \\)) is the same as the ratio of the volume of the voids (\\( V_v \\)) to the total volume (\\( V \\)), i.e., equal to porosity (\\( n \\)).\n\nHence,","source":"ocr_qwen2_vl_72b"},{"kind":"clip","index":2,"vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30.json#####audio#####doingASR#####FinishASR/---DC2PP_TI/307.6_336.18.mp4","text":"Let's consider the velocity. If we take the area of voids as A_V, then the area of voids multiplied by the actual velocity through the voids equals the total area times the superficial velocity. Here, V_EA represents the actual velocity of the flow.","source":"refined_asr"},{"kind":"clip","index":2,"vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Groundwater 

[
  "b'\\xff\\xd8\\xff\\xe0\\x00\\x10JFIF\\x00\\x01\\x02\\x00\\x00\\x01\\x00\\x01\\x00\\x00\\xff\\xfe\\x00\\x11Lavc58.134.100\\x00\\xff\\xdb\\x00C\\x00\\x08\\x10\\x10\\x13\\x10\\x13\\x16\\x16\\x16\\x16\\x16\\x16\\x1a\\x18\\x1a\\x1b\\x1b\\x1b\\x1a\\x1a\\x1a\\x1a\\x1b\\x1b\\x1b\\x1d\\x1d\\x1d\"\"\"\\x1d\\x1d\\x1d\\x1b\\x1b\\x1d\\x1d  \"\"%&%##\"#&&(((00..88:EES\\xff\\xc4\\x00\\xa4\\x00\\x01\\x00\\x02\\x03\\x01\\x01\\x01\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x06\\x05\\x03\\x04\\x02\\x01\\x07\\x08\\x01\\x01\\x00\\x02\\x03\\x01\\x01\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x01\\x06\\x02\\x04\\x05\\x03\\x07\\x10\\x00\\x02\\x02\\x01\\x02\\x03\\x07\\x03\\x02\\x04\\x02\\x06\\x08\\x05\\x04\\x03\\x00\\x01\\x03\\x02\\x11\\x04\\x121\\x13!Q\"q2A\\x91\\x05\\x81\\x14aRB\\xb1\\xa1#\\x153\\xb2rb$4\\xd1\\xc1\\x82\\x06CS\\x92\\xf0s5\\xa2\\xe1\\xf1t%\\xb3\\xc3DcF\\x16\\x83\\x11\\x01\\x00\\x02\\x02\\x01\\x03\\x03\\x03\\x05\\x01\\x01\\x01\\x00\\x00\\x00\\x00\\x00\\x01\\x02\\x11\\x03\\x04!1\\x12aQA\"\\x13q3\\xb12\\x91\\x81B\\xc1#\\xff\\xc0\\x00\\x11\\x08\\x02\\xd0\\x05\\x00\\x03\\x01\"\\x00\\x02\\x11\\x00\\x03\\x11\\x00\\xff\\xda\\x00\\x0c\\x03\\x01\\x00\\x02\\x11\\x03\\x11\\x00?\\x00\\xfb\\xbdk]\\xab\\xa2\\xe0\\xbd\\x11\\x93m{\\x17\\xb2\\x15\\xf2\\xaf\\x04v\\x07\\x1bk\\xd8\\xbd\\x90\\xdb^\\xc5\\xec\\x8c\\x87\\x80c\\xdb^\\xc5\\xec\\x86\\xda\\xf6/dd\\x00c\\xdb^\\xc5\\xec\\x86\\xda\\xf6/dd\\x00c\\xdb^\\xc5\\xec\\x86\\xda\\xf6/dd\\x00c\\xdb^\\xc5\\xec\\x86\\xda\\xf6/dd\\x00c\\xdb^\\xc5\\xec\\x86\\xda\\xf6/dd\\x00c\\xdb^\\xc5\\xec\\x86\\xda\\xf6/dd\\x00c\\xdb^\\xc5\\xec\\x86\\xda\\xf6/dd\\x00c\\xdb^\\xc5\\xec\\x86\\xda\\xf6/dd\\x00c\\xdb^\\xc5\\xec\\x86\\xda\\xf6/dd\\x00c\\xdb^\\xc5\\xec\\x86\\xda\\xf6/dd\\x00c\\xdb^\\xc5\\xec\\x86\\xda\\xf6/dd\\x00c\\xdb^\\xc5\\xec\\x86\\xda\\xf6/dd\\x00c\\xdb^\\xc5\\xec\\x86\\xda\\xf6/dd\\x00c\\xdb^\\xc5\\xec\\x86\\xda\\xf6/dd\\x00c\\xdb^\\xc5\\xec\\x86\\xda\\xf6/dd\\x00c\\xdb^\\xc5\\xec\\x86\\xda\\xf6/dd\\x00c\\xdb^\\xc5\\xec\\x86\\xda\\xf6/de<\\x03\\x8d\\xb5\\xfd+\\xd9\\r\\xb5\\xfd+\\xd9\\x1d\\x808\\xdb_\\xd2\\xbd\\x90\\xdb_\\xd2\\xbd\\x91\\xd8\\x03\\x8d\\xb5\\xfd+\\xd9\\r\\xb5\\xfd+\\xd9\\x1d\\x808\\xdb_\\xd2\\xbd\\x90\\xdb_\\xd2\\xbd\\x91\\xd8\\x03\\x8d\\xb5\\xfd+\\xd9\\r\\xb5\\xfd+\\xd9\\x1d\\x808\\xdb_\\xd2\\xbd\\x90\\xdb_\\xd2\\xbd\\x91\\xd8\\x03\\x8d\\xb5\\xfd+\\xd9\\r\\xb5\\xfd+\\xd9\\x1d\\x808\\xdb_\\xd2\\xbd\\x90\\xdb_\\xd2\\xbd\\x91\\xd8\\x03\\x8d\\xb5\\xfd+\\xd9\\r\\xb5\\xfd+\\xd9\\x1d\\x808\\xdb_\\xd2\\xbd\\x90\\xdb_\\xd2\\xbd\\x91\\xd8\\x03\\x8d\\xb5\\xfd+\\xd9\\r\\xb5\\xfd+\\xd9\\x1d\\x808\\xdb_\\xd2\\xbd\\x90\\xdb_\\xd2\\xbd\\x91\\xd8\\x03\\x8d\\xb5\\xfd+\\xd9\\r\\xb5\\xfd+\\xd9\\x1d\\x808\\xdb_\\xd2\\xbd\\x90\\xdb_\\xd2\\xbd\\x91\\xd8\\x03\\x8d\\xb5\\xfd+\\xd9\\r\\xb5\\xfd+\\xd9\\x1d\\x808\\xdb_\\xd2\\xbd\\x90\\xdb_\\xd2\\xbd\\x91\\xd8\\x03\\x8d\\xb5\\xfd+\\xd9\\r\\xb5\\xfd+\\xd9\\x1d\\x808\\xdb_\\xd2\\xbd\\x90\\xdb_\\xd2\\xbd\\x91\\xd8\\x03\\x8d\\xb5\\xfd+\\xd9\\r\\xb5\\xfd+\\xd9\\x1d\\x808\\xdb_\\xd2\\xbd\\x90\\xdb_\\xd2\\xbd\\x91\\xd8\\x03\\x8d\\xb5\\xfd+\\xd9\\r\\xb5\\xfd+\\xd9\\x1d\\x801\\xec\\xaf\\xe9^\\xc8\\xf7m\\x7fJ\\xf6G`\\x0e6\\xd7\\xf4\\xafd6\\xd7\\xf4\\xafdv\\x00\\xe3m\\x7fJ\\xf6Cm\\x7fJ\\xf6G`\\x0e6\\xd7\\xf4\\xafd6\\xd7\\xf4\\xafdv\\x00\\xe3m\\x7fJ\\xf6Cm\\x7fJ\\xf6G`\\x0e6\\xd7\\xf4\\xafd6\\xd7\\xf4\\xafdv\\x00\\xe3m\\x7fJ\\xf6Cm\\x7fJ\\xf6G`\\x0e6\\xd7\\xf4\\xafd6\\xd7\\xf4\\xafdv\\x00\\xe3m\\x7fJ\\xf6Cm\\x7fJ\\xf6G`\\x0e6\\xd7\\xf4\\xafdy\\xb6\\xbf\\xa5{# \\x03\\x16\\xca\\xfe\\x95\\xec\\x8d{\\xd25\\x8b:\\xae\\xef\\xe0\\xdd<\\x08j\\xe3\\x86)\\\\z\\x9el[\\xb3\\xd3\\xc3\\x0b\\x06[&\\xd3I\\xe1\\xfa3\\x1d\\x92\\xc6m\\xd7\\x1dC\\x07)F\\x9e\\xd5T\\xbdxt=U\\xdc\\x9ekU\\xd8\\xd1\\xee[I\\xd5g8\\xe3\\xd3\\xa1\\xd6\\x1e\\xe4\\xf3\\x85\\xd8\\x12\\xc7\\xcb\\xae\\xdc4\\xad\\x8e\\xd4\\x8f::\\xe6\\xb5O\\xc5`\\xeb\\xbb[c\\xaem\\xd4\\xc8\\xb7e\\xe5t\\xf4\\x08a\\xb5+\\xd1\\xf4X\\xe3\\xd1\\x1e\\xba\\xd2\\xad[bm\\xf4\\xca_\\xf9\\xe8t\\xab\\xd3\\r\\xee\\xe3\\xc4\\xf5[5\\xcd\\x7f

[{"image_index":0,"interleaved_index":0,"member_name":"dataset_images_interval_7/---DC2PP_TI/[email protected]_276.96#1.jpg","source_image_path":"/mnt/workspace/zwq_data/interleaved_dataset/dataset_images_interval_7/---DC2PP_TI/[email protected]_276.96#1.jpg","caption":"We can see these text from the image: Dividing both sides of equation by A, we get\n\nwhere v is the discharge velocity, and is not the actual flow velocity through the soil medium, since the flow occurs through the voids of cross-sectional area A, and not in A itself. The permeability of the soil can then be viewed as this superficial velocity under a unit hydraulic gradient.\n\nIf A is the area of the voids, then\n\nwhere Va is the actual velocity of flow of water through the soil. Then\n\nwhen A is large in comparison, we can safely assume that the ratio of the area of the void(Av) to the total area (A) is the same as the ratio of the volume of the voids (Vv)to the total volume (V), i.e. equal to porosity (n).\n\nHence,.\n It's equal to K. If we divide both sides of the equation by the area, it becomes Q over A is equal to K times IA over A. So this A cancels out. From here, this Q over A, which is discharge over area, is known as velocity V, and it's equal to K times I.","caption_source":"text_ocr","caption_distance":1,"image_byte_len":49734,"image_sha256":"5c3f4185067b4ca226ae78d76c6ece425da32d9107b15b8c042712cdcf5db42f","image_width":1280,"image_height":720,"token_estimate":3600,"dhash":"1501294159012101","vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30.json#####audio#####doingASR#####FinishASR/---DC2PP_TI/247.6_276.96.mp4","source_record_index":283293,"sample_id":"4e816eaa58fa8ea4ac3465fa","crop":{"source_record_index":283293,"frame_index":0,"frame_available":true,"orig_width":1280,"orig_height":720,"crop_status":"accepted","crop_box_x":0,"crop_box_y":0,"crop_box_w":1280,"crop_box_h":712,"crop_confidence":0.6642669698209489,"crop_candidate":"ocr_tight:boxes=18","crop_candidate_count":4,"crop_text_mass":1.0,"crop_visual_text_mass":0.9994084179216813,"crop_ocr_box_recall":1.0,"crop_ocr_area_recall":1.0,"crop_ocr_cut_count":0.0,"crop_ocr_box_count":18.0,"crop_ocr_status":"ok:easyocr:18","crop_relevance":0.9797042089608408,"crop_reason":"accepted: mode=content confidence=0.664 area_ratio=0.989 score_mass=0.999 text_mass=1.000 visual_text_mass=0.999 ocr_box_recall=1.000 ocr_area_recall=1.000 ocr_cuts=0 ocr_status=ok:easyocr:18 relevance=0.980 x_mass=0.912 y_mass=0.925 candidate=ocr_tight:boxes=18 context=0.60:content_terms,gesture_terms","crop_preview_rel":"","orig_preview_rel":"","failure_flags":[]}},{"image_index":1,"interleaved_index":2,"member_name":"dataset_images_interval_7/---DC2PP_TI/[email protected]_307.20000000000005#1.jpg","source_image_path":"/mnt/workspace/zwq_data/interleaved_dataset/dataset_images_interval_7/---DC2PP_TI/[email protected]_307.20000000000005#1.jpg","caption":"We can see these text from the image: Dividing both sides of equation by A, we get\n\nwhere v is the discharge velocity, and is not the actual flow velocity through the soil medium, since the flow occurs through the voids of cross-sectional area A, and not in A itself. The permeability of the soil can then be viewed as this superficial velocity under a unit hydraulic gradient.\n\nIf A is the area of the voids, then\n\nwhere Va is the actual velocity of flow of water through the soil. Then\n\nwhen A is large in comparison, we can safely assume that the ratio of the area of the void(Av) to the total area (A) is the same as the ratio of the volume of the voids (Vv)to the total volume (V), i.e. equal to porosity (n).\n\nHence,.\n It's equal to K. If we divide both sides of the equation by the area, it becomes Q over A is equal to K times IA over A. So this A cancels out. From here, this Q over A, which is discharge over area, is known as velocity V,

9

bec63daedf14a3606d33f901

Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30

396.18_419.58

Out of Dufaitz and the Themes theory we usually discuss the Themes theory first and then the discussion of Dufaitz theory is carried out. After studying the Themes theory it's a bit easier to study about Dufaitz. In Dufaitz what are the changes than the themes? First change is that there are no observations.

Dupuit's…

https://www.youtube.com/watch?v=---DC2PP_TI

[]

Out of Dufaitz and the Themes theory we usually discuss the Themes theory first and then the discussion of Dufaitz theory is carried out. After studying the Themes theory it's a bit easier to study about Dufaitz. In Dufaitz what are the changes than the themes? First change is that there are no observations.

Dupuit's theory

We will now discuss the original Dupuit's formulas. In Dupuit's formulas, no observation wells (as constructed in Thiem's formula) are constructed. The main well is pumped out so as to get sufficient drawdown, and then the rate of pumping is so adjusted as to establish equilibrium conditions (i.e., the rate of inflow becomes equal to the rate of outflow, and the water level in the well becomes constant).

All the assumptions which have been made in the Theim's formulas hold good on the Dupuit's formulas also. The only difference is that the integration which was done the limits of r1 and r2 (radii of two observation wells) in Theim's formulas is changed, and the integration is done between the limits \( r_w \) and R, where \( r_w \) is the radius of the main pumped well and R is the radius of influence.

The radius of influence is the distance from the centre of the pumped well to the point, where the drawdown is zero or is inappreciable.

Well in the case of the Dupuit theory as was in the case of Thiem's formula the main well is pumped out so as to get sufficient drawdown and then the rate of pumping is so adjusted as to establish the equilibrium condition that is the steady state is achieved that is the rate.

Dupuit’s theory

We will now discuss the original Dupuit’s formulas. In Dupuit’s formulas, no observation wells (as constructed in Thiem’s formula) are constructed. The main well is pumped out so as to get sufficient drawdown, and then the rate of pumping is so adjusted as to establish equilibrium conditions (i.e., the rate of inflow becomes equal to the rate of outflow, and the water level in the well becomes constant).

All the assumptions which have been made in the Theim’s formulas hold good on the Dupuit’s formulas also. The only difference is that the integration which was done the limits of r1 and r2 (radii of two observation wells) in Theim’s formulas is changed, and the integration is done between the limits \( r_w \) and R, where \( r_w \) is the radius of the main pumped well and R is the radius of influence.

The radius of influence is the distance from the centre of the pumped well to the point, where the drawdown is zero or is inappreciable.

The inflow becomes equal to the rate of outflow. And if this happens, the water level in the well becomes constant. Now, all the assumptions we've made in the Theis theory hold true in the Dupit theory as well. The only difference here will be that instead of the limits,

Which we used in the Theis theory, R1 and R2, which were the radii of the two observation wells. Here we will be integrating it in the range of Rw to R, where Rw is the radius of the main pumped well and R is the radius of the influence. Now, what is this radius of influence? It is:

The distance from the center of the pumped well to the point where the drawdown is zero or isn't appreciable, that means where the drawdown has completely been eliminated. Now we know that we are having two types of aquifers. One is the

Dupuit's theory

We will now discuss the original Dupuit's formulas. In Dupuit's formulas, no observation wells (as constructed in Thiem's formula) are constructed. The main well is pumped out so as to get sufficient drawdown, and then the rate of pumping is so adjusted as to establish equilibrium conditions (i.e., the rate of inflow becomes equal to the rate of outflow, and the water level in the well becomes constant).

All the assumptions which have been made in the Thiem's formulas hold good on the Dupuit's formulas also. The only difference is that the integration which was done the limits of r1 and r2 (radii of two observation wells) in Thiem's formulas is c

862

12

2

4670

[{"kind":"clip","index":0,"vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30.json#####audio#####doingASR#####FinishASR/---DC2PP_TI/396.18_419.58.mp4","text":"Out of Dufaitz and the Themes theory we usually discuss the Themes theory first and then the discussion of Dufaitz theory is carried out. After studying the Themes theory it's a bit easier to study about Dufaitz. In Dufaitz what are the changes than the themes? First change is that there are no observations.","source":"refined_asr"},{"kind":"clip","index":0,"vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30.json#####audio#####doingASR#####FinishASR/---DC2PP_TI/396.18_419.58.mp4","text":"Dupuit's theory\n\nWe will now discuss the original Dupuit's formulas. In Dupuit's formulas, no observation wells (as constructed in Thiem's formula) are constructed. The main well is pumped out so as to get sufficient drawdown, and then the rate of pumping is so adjusted as to establish equilibrium conditions (i.e., the rate of inflow becomes equal to the rate of outflow, and the water level in the well becomes constant).\n\nAll the assumptions which have been made in the Theim's formulas hold good on the Dupuit's formulas also. The only difference is that the integration which was done the limits of r1 and r2 (radii of two observation wells) in Theim's formulas is changed, and the integration is done between the limits \\( r_w \\) and R, where \\( r_w \\) is the radius of the main pumped well and R is the radius of influence.\n\nThe radius of influence is the distance from the centre of the pumped well to the point, where the drawdown is zero or is inappreciable.","source":"ocr_qwen2_vl_72b"},{"kind":"clip","index":1,"vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30.json#####audio#####doingASR#####FinishASR/---DC2PP_TI/419.58_444.5.mp4","text":"Well in the case of the Dupuit theory as was in the case of Thiem's formula the main well is pumped out so as to get sufficient drawdown and then the rate of pumping is so adjusted as to establish the equilibrium condition that is the steady state is achieved that is the rate.","source":"refined_asr"},{"kind":"clip","index":1,"vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30.json#####audio#####doingASR#####FinishASR/---DC2PP_TI/419.58_444.5.mp4","text":"Dupuit’s theory\n\nWe will now discuss the original Dupuit’s formulas. In Dupuit’s formulas, no observation wells (as constructed in Thiem’s formula) are constructed. The main well is pumped out so as to get sufficient drawdown, and then the rate of pumping is so adjusted as to establish equilibrium conditions (i.e., the rate of inflow becomes equal to the rate of outflow, and the water level in the well becomes constant).\n\nAll the assumptions which have been made in the Theim’s formulas hold good on the Dupuit’s formulas also. The only difference is that the integration which was done the limits of r1 and r2 (radii of two observation wells) in Theim’s formulas is changed, and the integration is done between the limits \\( r_w \\) and R, where \\( r_w \\) is the radius of the main pumped well and R is the radius of influence.\n\nThe radius of influence is the distance from the centre of the pumped well to the point, where the drawdown is zero or is inappreciable.","source":"ocr_qwen2_vl_72b"},{"kind":"clip","index":2,"vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30.json#####audio#####doingASR#####FinishASR/---DC2PP_TI/444.5_467.8.mp4","text":"The inflow becomes equal to the rate of outfl

[
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[{"image_index":0,"interleaved_index":0,"member_name":"dataset_images_interval_7/---DC2PP_TI/[email protected]_419.58#1.jpg","source_image_path":"/mnt/workspace/zwq_data/interleaved_dataset/dataset_images_interval_7/---DC2PP_TI/[email protected]_419.58#1.jpg","caption":"We can see these text from the image: Dupuit's theory\n\nWe will now discuss the original Dupuit's formulas. In Dupuit's formulas, no observation wells (as constructed in Thiem's formula) are constructed. The main well is pumped out so as to get sufficient drawdown, and then the rate of pumping is so adjusted as to establish equilibrium conditions (i.e., the rate of inflow becomes equal to the rate of outflow, and the water level in the well becomes constant).\n\nAll the assumptions which have been made in the Theim's formulas hold good on the Dupuit's formulas also. The only difference is that the integration which was done the limits of r1 and r2 (radii of two observation wells) in Theim's formulas is changed, and the integration is done between the limits \\( r_w \\) and R, where \\( r_w \\) is the radius of the main pumped well and R is the radius of influence.\n\nThe radius of influence is the distance from the centre of the pumped well to the point, where the drawdown is zero or is inappreciable..\n Out of Dufaitz and the Themes theory we usually discuss the Themes theory first and then the discussion of Dufaitz theory is carried out. After studying the Themes theory it's a bit easier to study about Dufaitz. In Dufaitz what are the changes than the themes? First change is that there are no observations.","caption_source":"text_ocr","caption_distance":1,"image_byte_len":64982,"image_sha256":"b9eb854809edba2e218e6729210b5d7a1b078344129ffb2750ed66d549b853f5","image_width":1280,"image_height":720,"token_estimate":3600,"dhash":"0541551381010141","vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30.json#####audio#####doingASR#####FinishASR/---DC2PP_TI/396.18_419.58.mp4","source_record_index":283294,"sample_id":"bec63daedf14a3606d33f901","crop":{"source_record_index":283294,"frame_index":0,"frame_available":true,"orig_width":1280,"orig_height":720,"crop_status":"accepted","crop_box_x":0,"crop_box_y":0,"crop_box_w":1280,"crop_box_h":544,"crop_confidence":0.7571485944054133,"crop_candidate":"ocr_tight:boxes=19","crop_candidate_count":4,"crop_text_mass":1.0,"crop_visual_text_mass":0.9979027220921183,"crop_ocr_box_recall":1.0,"crop_ocr_area_recall":1.0,"crop_ocr_cut_count":0.0,"crop_ocr_box_count":19.0,"crop_ocr_status":"ok:easyocr:19","crop_relevance":0.9789513610460592,"crop_reason":"accepted: mode=content confidence=0.757 area_ratio=0.756 score_mass=0.998 text_mass=1.000 visual_text_mass=0.998 ocr_box_recall=1.000 ocr_area_recall=1.000 ocr_cuts=0 ocr_status=ok:easyocr:19 relevance=0.979 x_mass=0.910 y_mass=0.914 candidate=ocr_tight:boxes=19 context=0.60:content_terms,gesture_terms","crop_preview_rel":"","orig_preview_rel":"","failure_flags":[]}},{"image_index":5,"interleaved_index":9,"member_name":"dataset_images_interval_7/---DC2PP_TI/[email protected]_514.24#3.jpg","source_image_path":"/mnt/workspace/zwq_data/interleaved_dataset/dataset_images_interval_7/---DC2PP_TI/[email protected]_514.24#3.jpg","caption":"We can see these text from the image: Dupuit's theory\n\nWe will now discuss the original Dupuit's formulas. In Dupuit's formulas, no observation wells (as constructed in Thiem's formula) are constructed. The main well is pumped out so as to get sufficient drawdown, and then the rate of pumping is so adjusted as to establish equilibrium conditions (i.e., the rate of inflow becomes equal to the rate of outflow, and the water level in the well becomes constant).\n\nAll the assumptions which have been made in the Thiem's formulas hold good on the Dupuit's formulas also. The only difference is that the integration which was done the limits of r1 and r2 (radii 

10

3763787009de1474d1453930

Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30

533.36_552.62

The layer is free. Therefore, we can easily extract the water out of this. As we start extracting the water, the water level drops down to this HW level. The same profile is maintained up to the last point of the drawdown.

- Dupuit's Formula for unconfined aquifer
- GROUND
- W.T.
- d=SATURATED THICKNESS OF THE AQUIFE…

https://www.youtube.com/watch?v=---DC2PP_TI

[]

The layer is free. Therefore, we can easily extract the water out of this. As we start extracting the water, the water level drops down to this HW level. The same profile is maintained up to the last point of the drawdown.

- Dupuit's Formula for unconfined aquifer
- GROUND
- W.T.
- d=SATURATED THICKNESS OF THE AQUIFER
- h_w
- R
- w

So this shape, which is observed, is known as the cone of depression. Now we know that this discharge is equal to K times I times A, where I is the hydraulic gradient. If we consider a small section for that, the height of the water level is dH for the length of dr, the area of this.

- Dupuit’s Formula for unconfined aquifer
- GROUND
- W.T.
- CONE OF DEPRESSION
- d=SATURATED THICKNESS OF THE AQUIFER

The formula for a cylinder is 2πrh. Here, k is the coefficient of permeability. Now, if we rearrange the terms, it becomes dr/r = 2πk/q * h dh. We need to integrate this with respect to dh.

- Dupuit's Formula for unconfined aquifer
- GROUND
- CONE OF DEPRESSION
- d=SATURATED THICKNESS OF THE AQUIFER
- Q = K . i . A
- = K . dh . 2πrh / dr

Equation. So the radius will be varying for the main well. This is the main well having the radius R sub w. And this is the point where the influence zone is eliminated. So this radius is known as the radius of influence denoted by capital R. So the limits will be R sub w to R for the level of water from H sub w to the. It seems like the sentence was cut off at the end and might need further clarification or continuation.

- Dupuit’s Formula for unconfined aquifer
- GROUND
- W.T.
- CONE OF DEPRESSION
- d=SATURATED THICKNESS OF THE AQUIFER
- Q = K . i . A
- Q = K . dh . 2πrh
- ∫ dr = 2πK ∫ h dh

Complete level that is D. So if we integrate this, what we are getting is the natural log of R. Now limits for this are from R lowercase W to capital R, then 2 Pi K upon Q. This is H square by 2. Limits are written as equal to the size of the entire height of the base. So this:

- Dupuit's Formula for unconfined aquifer
- GROUND
- W.T.
- CONE OF DEPRESSION
- d=SATURATED THICKNESS OF THE AQUIFER
- Q = K . i . A
- Q = K . dh / dr . 2πr h
- ∫(dh / h) from hw to R = (2πK / Q) ∫h dh from hw to R

From h sub w to d. So this will be natural log of capital R over r sub w equals this. The twos will cancel out. So it will be pi k over q, integrated from d squared minus h sub w squared. Therefore, the rate of flow, if we summarize it, will be pi k into d squared minus h sub w.

\[
\ln \left( r \right)_{R} = \frac{2 \pi K}{Q} \left( \frac{h^2}{2} \right)_{d}
\]

504

12

5

2546

[{"kind":"clip","index":0,"vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30.json#####audio#####doingASR#####FinishASR/---DC2PP_TI/533.36_552.62.mp4","text":"The layer is free. Therefore, we can easily extract the water out of this. As we start extracting the water, the water level drops down to this HW level. The same profile is maintained up to the last point of the drawdown.","source":"refined_asr"},{"kind":"clip","index":0,"vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30.json#####audio#####doingASR#####FinishASR/---DC2PP_TI/533.36_552.62.mp4","text":"- Dupuit's Formula for unconfined aquifer\n- GROUND\n- W.T.\n- d=SATURATED THICKNESS OF THE AQUIFER\n- h_w\n- R\n- w","source":"ocr_qwen2_vl_72b"},{"kind":"clip","index":1,"vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30.json#####audio#####doingASR#####FinishASR/---DC2PP_TI/552.62_581.7.mp4","text":"So this shape, which is observed, is known as the cone of depression. Now we know that this discharge is equal to K times I times A, where I is the hydraulic gradient. If we consider a small section for that, the height of the water level is dH for the length of dr, the area of this.","source":"refined_asr"},{"kind":"clip","index":1,"vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30.json#####audio#####doingASR#####FinishASR/---DC2PP_TI/552.62_581.7.mp4","text":"- Dupuit’s Formula for unconfined aquifer\n- GROUND\n- W.T.\n- CONE OF DEPRESSION\n- d=SATURATED THICKNESS OF THE AQUIFER","source":"ocr_qwen2_vl_72b"},{"kind":"clip","index":2,"vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30.json#####audio#####doingASR#####FinishASR/---DC2PP_TI/581.7_603.32.mp4","text":"The formula for a cylinder is 2πrh. Here, k is the coefficient of permeability. Now, if we rearrange the terms, it becomes dr/r = 2πk/q * h dh. We need to integrate this with respect to dh.","source":"refined_asr"},{"kind":"clip","index":2,"vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30.json#####audio#####doingASR#####FinishASR/---DC2PP_TI/581.7_603.32.mp4","text":"- Dupuit's Formula for unconfined aquifer\n- GROUND\n- CONE OF DEPRESSION\n- d=SATURATED THICKNESS OF THE AQUIFER\n- Q = K . i . A\n- = K . dh . 2πrh / dr","source":"ocr_qwen2_vl_72b"},{"kind":"clip","index":3,"vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30.json#####audio#####doingASR#####FinishASR/---DC2PP_TI/603.5_634.4.mp4","text":"Equation. So the radius will be varying for the main well. This is the main well having the radius R sub w. And this is the point where the influence zone is eliminated. So this radius is known as the radius of influence denoted by capital R. So the limits will be R sub w to R for the level of water from H sub w to the. It seems like the sentence was cut off at the end and might need further clarification or continuation.","source":"refined_asr"},{"kind":"clip","index":3,"vid":"---DC2PP_TI.mp4","clip_path":"/mnt/workspace/zwq_data/youtube_interleave/video_clip/Groundwater Hydrology Tutorial on Groundwater Flow Velocity_30.json#####audio#####doingASR#####FinishASR/---DC2PP_TI/603.5_634.4.mp4","text":"- Dupuit’s Formula for unconfined aquifer\n- GROUND\n- W.T.\n- CONE OF DEPRESSION\n- d=SATURATED THICKNESS OF THE AQUIFER\n- Q = K . i . A\n- Q = K . dh . 2πrh\n- ∫ dr = 2πK ∫ h dh","source":"ocr_qwen2_vl_72b"},{"kind":

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