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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...
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 commonly used to calculate the flow rate, velocity, or diameter of a pipe. It is expressed as:
Q = (1/n) * A * R^(2/3) * S^(1/2)
where:
Q = Flow rate (m^3/s)
n = Manning friction factor
A = Cross-sectional area of the pipe (m^2)
R = Hydraulic radius (m)
S = Hydraulic gradient or slope (m/m)
Calculating the hydraulic radius (R):
The hydraulic radius is defined as the ratio of the cross-sectional area to the wetted perimeter of the pipe. In a fully developed flow, the pipe is assumed to be circular, so the wetted perimeter is equal to the circumference of the pipe.
Formula:
R = A/P
where:
P = Wetted perimeter (m)
Calculating the wetted perimeter (P):
The wetted perimeter is the length of the pipe in contact with the flowing water. For a circular pipe, the wetted perimeter is equal to the circumference.
Formula:
P = 2πr
where:
r = Radius of the pipe (m)
Substituting the values:
P = 2πr
Calculating the cross-sectional area (A):
The cross-sectional area of a circular pipe is given by the formula:
Formula:
A = πr^2
Substituting the values:
A = πr^2
Calculating the hydraulic radius (R):
R = A/P
Substituting the values:
R = A/(2πr)
Using the Manning formula:
Q = (1/n) * A * R^(2/3) * S^(1/2)
Substituting the given values:
2 = (1/0.25) * A * R^(2/3) * S^(1/2)
Calculating the diameter of the pipe:
Since we are required to find the diameter of the pipe, we can use the formula for the cross-sectional area of a circular pipe to determine the value of A.
Substituting the value of A in terms of diameter (D):
A = π(D^2)/4
Substituting the value of A in the Manning formula:
2 = (1/0.25) * (π(D^2)/4) * R^(2/3) * S^(1/2)
Simplifying the equation:
8 = π * D^2 * R^(2/3) * S^(1/2)
Substituting the value of R in terms of D:
R = A/(2πr)
R = (π(D^2)/4)/(2πr)
R = D/4r
Substituting the value of R in the equation:
8 = π * D^2 * (
- 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 commonly used to calculate the flow rate, velocity, or diameter of a pipe. It is expressed as:
Q = (1/n) * A * R^(2/3) * S^(1/2)
where:
Q = Flow rate (m^3/s)
n = Manning friction factor
A = Cross-sectional area of the pipe (m^2)
R = Hydraulic radius (m)
S = Hydraulic gradient or slope (m/m)
Calculating the hydraulic radius (R):
The hydraulic radius is defined as the ratio of the cross-sectional area to the wetted perimeter of the pipe. In a fully developed flow, the pipe is assumed to be circular, so the wetted perimeter is equal to the circumference of the pipe.
Formula:
R = A/P
where:
P = Wetted perimeter (m)
Calculating the wetted perimeter (P):
The wetted perimeter is the length of the pipe in contact with the flowing water. For a circular pipe, the wetted perimeter is equal to the circumference.
Formula:
P = 2πr
where:
r = Radius of the pipe (m)
Substituting the values:
P = 2πr
Calculating the cross-sectional area (A):
The cross-sectional area of a circular pipe is given by the formula:
Formula:
A = πr^2
Substituting the values:
A = πr^2
Calculating the hydraulic radius (R):
R = A/P
Substituting the values:
R = A/(2πr)
Using the Manning formula:
Q = (1/n) * A * R^(2/3) * S^(1/2)
Substituting the given values:
2 = (1/0.25) * A * R^(2/3) * S^(1/2)
Calculating the diameter of the pipe:
Since we are required to find the diameter of the pipe, we can use the formula for the cross-sectional area of a circular pipe to determine the value of A.
Substituting the value of A in terms of diameter (D):
A = π(D^2)/4
Substituting the value of A in the Manning formula:
2 = (1/0.25) * (π(D^2)/4) * R^(2/3) * S^(1/2)
Simplifying the equation:
8 = π * D^2 * R^(2/3) * S^(1/2)
Substituting the value of R in terms of D:
R = A/(2πr)
R = (π(D^2)/4)/(2πr)
R = D/4r
Substituting the value of R in the equation:
8 = π * D^2 * (
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Community Answer
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 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 Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) 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 Electrical Engineering (EE) 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 Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) 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 Electrical Engineering (EE) 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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