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To replace a pipe of diameter D by n parallel pipes of diameter d, the formula used is
- a)d = D/n
- b)d = D/n1/2
- c)d = D/n3/2
- d)d = D/n2/5
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
To replace a pipe of diameter D by n parallel pipes of diameter d, th...
The main pipeline divides into two or more parallel pipes, which again join together downstream.
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Q = Q1 + Q2
For n parallel pipes of diameter d, d = D/n2/5
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To replace a pipe of diameter D by n parallel pipes of diameter d, th...
The main pipeline divides into two or more parallel pipes, which again join together downstream.
Q = Q1 + Q2
For n parallel pipes of diameter d, d = D/n2/5
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To replace a pipe of diameter D by n parallel pipes of diameter d, th...
Replacing a Pipe with Parallel Pipes
To replace a pipe of diameter D with n parallel pipes of diameter d, the formula used is:
d = D/n^0.4
Explanation:
- The formula for the hydraulic diameter of a pipe is given by:
Dh = 4A/P
where Dh is the hydraulic diameter, A is the cross-sectional area of the pipe, and P is the wetted perimeter of the pipe. For a circular pipe, the hydraulic diameter is simply the diameter of the pipe.
- The formula for the flow rate (Q) through a pipe is given by:
Q = (π/4)D^2v
where v is the velocity of the fluid in the pipe.
- If we replace the single pipe of diameter D with n parallel pipes of diameter d, the total cross-sectional area of the parallel pipes is n times the cross-sectional area of the single pipe. Therefore, the velocity of the fluid in the parallel pipes will be n times less than the velocity in the single pipe to maintain the same flow rate (Q).
- Using the continuity equation, we can relate the velocity of the fluid to the cross-sectional area of the pipe:
Q = Av
where A is the cross-sectional area of the pipe.
- Combining the above equations, we get:
(π/4)D^2v = n(π/4)d^2(v/n)
Simplifying this equation, we get:
d = D/n^0.4
Therefore, the formula used to replace a pipe of diameter D with n parallel pipes of diameter d is:
d = D/n^0.4
To replace a pipe of diameter D with n parallel pipes of diameter d, the formula used is:
d = D/n^0.4
Explanation:
- The formula for the hydraulic diameter of a pipe is given by:
Dh = 4A/P
where Dh is the hydraulic diameter, A is the cross-sectional area of the pipe, and P is the wetted perimeter of the pipe. For a circular pipe, the hydraulic diameter is simply the diameter of the pipe.
- The formula for the flow rate (Q) through a pipe is given by:
Q = (π/4)D^2v
where v is the velocity of the fluid in the pipe.
- If we replace the single pipe of diameter D with n parallel pipes of diameter d, the total cross-sectional area of the parallel pipes is n times the cross-sectional area of the single pipe. Therefore, the velocity of the fluid in the parallel pipes will be n times less than the velocity in the single pipe to maintain the same flow rate (Q).
- Using the continuity equation, we can relate the velocity of the fluid to the cross-sectional area of the pipe:
Q = Av
where A is the cross-sectional area of the pipe.
- Combining the above equations, we get:
(π/4)D^2v = n(π/4)d^2(v/n)
Simplifying this equation, we get:
d = D/n^0.4
Therefore, the formula used to replace a pipe of diameter D with n parallel pipes of diameter d is:
d = D/n^0.4
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