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Consider a fully developed flow of water in a pipe. The velocity of flow is 2 m/s and dynamic viscosity is 1.5 Pa/s. If the value of manning friction factor is 0.25, then diameter of the pipe is __________ mm. (Answer up to the nearest integer)
Correct answer is '192'. Can you explain this answer?
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Consider a fully developed flow of water in a pipe. The velocity of f...
Manning friction factor is
As Reynolds number, Re < 2300,="" the="" flow="" is="" />
D = 0.192 m
= 192 mm
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Consider a fully developed flow of water in a pipe. The velocity of f...
Given data:
- Velocity of flow (V) = 2 m/s
- Dynamic viscosity (μ) = 1.5 Pa/s
- Manning friction factor (n) = 0.25
Formula:
The Manning formula is used to calculate the flow velocity in an open channel or pipe. It is given by:
Q = (1/n) * (A * R^(2/3)) * (S^(1/2))
Where:
- Q is the flow rate
- A is the cross-sectional area of flow
- R is the hydraulic radius
- S is the slope of the energy grade line
Calculating the flow area:
We know that the flow area (A) is equal to the cross-sectional area of the pipe, which can be calculated using the formula:
A = (π * D^2) / 4
Where:
- D is the diameter of the pipe
Calculating the hydraulic radius:
The hydraulic radius (R) is given by the formula:
R = A / P
Where:
- P is the wetted perimeter of the pipe
Calculating the wetted perimeter:
The wetted perimeter (P) can be calculated using the formula:
P = π * D
Calculating the slope of the energy grade line:
The slope of the energy grade line (S) can be calculated by equating the friction loss to the energy loss due to the slope:
S = (f * V^2) / (2 * g * D)
Where:
- f is the Darcy-Weisbach friction factor
- g is the acceleration due to gravity (9.81 m/s^2)
Calculating the Darcy-Weisbach friction factor:
The Darcy-Weisbach friction factor (f) can be calculated using the Manning friction factor (n) and the Reynolds number (Re):
f = (1 / (4 * n^2)) * (Re^0.63)
Calculating the Reynolds number:
The Reynolds number (Re) can be calculated using the formula:
Re = (V * D) / μ
Solving the equations:
1. Calculate the Reynolds number:
Re = (2 * D) / 1.5
2. Calculate the Darcy-Weisbach friction factor:
f = (1 / (4 * 0.25^2)) * ((2 * D) / 1.5)^0.63
3. Calculate the slope of the energy grade line:
S = (f * 2^2) / (2 * 9.81 * D)
4. Calculate the wetted perimeter:
P = π * D
5. Calculate the hydraulic radius:
R = (π * D^2) / (4 * π * D)
6. Calculate the flow area:
A = (π * D^2) / 4
7. Use the Manning formula to find the flow rate:
Q = (1/0.25) * (A * R^(2/3)) * (S^(1/2))
Calculating the diameter:
Since the flow rate (Q) is not given, we can set it equal to 1 for simplicity:
1 = (1/0.25
- Velocity of flow (V) = 2 m/s
- Dynamic viscosity (μ) = 1.5 Pa/s
- Manning friction factor (n) = 0.25
Formula:
The Manning formula is used to calculate the flow velocity in an open channel or pipe. It is given by:
Q = (1/n) * (A * R^(2/3)) * (S^(1/2))
Where:
- Q is the flow rate
- A is the cross-sectional area of flow
- R is the hydraulic radius
- S is the slope of the energy grade line
Calculating the flow area:
We know that the flow area (A) is equal to the cross-sectional area of the pipe, which can be calculated using the formula:
A = (π * D^2) / 4
Where:
- D is the diameter of the pipe
Calculating the hydraulic radius:
The hydraulic radius (R) is given by the formula:
R = A / P
Where:
- P is the wetted perimeter of the pipe
Calculating the wetted perimeter:
The wetted perimeter (P) can be calculated using the formula:
P = π * D
Calculating the slope of the energy grade line:
The slope of the energy grade line (S) can be calculated by equating the friction loss to the energy loss due to the slope:
S = (f * V^2) / (2 * g * D)
Where:
- f is the Darcy-Weisbach friction factor
- g is the acceleration due to gravity (9.81 m/s^2)
Calculating the Darcy-Weisbach friction factor:
The Darcy-Weisbach friction factor (f) can be calculated using the Manning friction factor (n) and the Reynolds number (Re):
f = (1 / (4 * n^2)) * (Re^0.63)
Calculating the Reynolds number:
The Reynolds number (Re) can be calculated using the formula:
Re = (V * D) / μ
Solving the equations:
1. Calculate the Reynolds number:
Re = (2 * D) / 1.5
2. Calculate the Darcy-Weisbach friction factor:
f = (1 / (4 * 0.25^2)) * ((2 * D) / 1.5)^0.63
3. Calculate the slope of the energy grade line:
S = (f * 2^2) / (2 * 9.81 * D)
4. Calculate the wetted perimeter:
P = π * D
5. Calculate the hydraulic radius:
R = (π * D^2) / (4 * π * D)
6. Calculate the flow area:
A = (π * D^2) / 4
7. Use the Manning formula to find the flow rate:
Q = (1/0.25) * (A * R^(2/3)) * (S^(1/2))
Calculating the diameter:
Since the flow rate (Q) is not given, we can set it equal to 1 for simplicity:
1 = (1/0.25
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Consider a fully developed flow of water in a pipe. The velocity of flow is 2 m/s and dynamic viscosity is 1.5 Pa/s. If the value of manning friction factor is 0.25, then diameter of the pipe is __________ mm. (Answer up to the nearest integer)Correct answer is '192'. Can you explain this answer?
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Consider a fully developed flow of water in a pipe. The velocity of flow is 2 m/s and dynamic viscosity is 1.5 Pa/s. If the value of manning friction factor is 0.25, then diameter of the pipe is __________ mm. (Answer up to the nearest integer)Correct answer is '192'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Consider a fully developed flow of water in a pipe. The velocity of flow is 2 m/s and dynamic viscosity is 1.5 Pa/s. If the value of manning friction factor is 0.25, then diameter of the pipe is __________ mm. (Answer up to the nearest integer)Correct answer is '192'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a fully developed flow of water in a pipe. The velocity of flow is 2 m/s and dynamic viscosity is 1.5 Pa/s. If the value of manning friction factor is 0.25, then diameter of the pipe is __________ mm. (Answer up to the nearest integer)Correct answer is '192'. Can you explain this answer?.
Consider a fully developed flow of water in a pipe. The velocity of flow is 2 m/s and dynamic viscosity is 1.5 Pa/s. If the value of manning friction factor is 0.25, then diameter of the pipe is __________ mm. (Answer up to the nearest integer)Correct answer is '192'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Consider a fully developed flow of water in a pipe. The velocity of flow is 2 m/s and dynamic viscosity is 1.5 Pa/s. If the value of manning friction factor is 0.25, then diameter of the pipe is __________ mm. (Answer up to the nearest integer)Correct answer is '192'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a fully developed flow of water in a pipe. The velocity of flow is 2 m/s and dynamic viscosity is 1.5 Pa/s. If the value of manning friction factor is 0.25, then diameter of the pipe is __________ mm. (Answer up to the nearest integer)Correct answer is '192'. Can you explain this answer?.
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Consider a fully developed flow of water in a pipe. The velocity of flow is 2 m/s and dynamic viscosity is 1.5 Pa/s. If the value of manning friction factor is 0.25, then diameter of the pipe is __________ mm. (Answer up to the nearest integer)Correct answer is '192'. Can you explain this answer?, a detailed solution for Consider a fully developed flow of water in a pipe. The velocity of flow is 2 m/s and dynamic viscosity is 1.5 Pa/s. If the value of manning friction factor is 0.25, then diameter of the pipe is __________ mm. (Answer up to the nearest integer)Correct answer is '192'. Can you explain this answer? has been provided alongside types of Consider a fully developed flow of water in a pipe. The velocity of flow is 2 m/s and dynamic viscosity is 1.5 Pa/s. If the value of manning friction factor is 0.25, then diameter of the pipe is __________ mm. (Answer up to the nearest integer)Correct answer is '192'. Can you explain this answer? theory, EduRev gives you an
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