
Concept explainers
The steady flow rates in each pipe.

Answer to Problem 6.124P
Explanation of Solution
Given information:
The fluid is water at
At three reservoir junction, if all flows are considered positive towards the junction, then
Assuming the gauge pressure
To solve this type of problems, we should guess the position of
If the
Calculation:
First of all,
Guess
The roughness ratio for pipe 1 will be,
To find Reynolds’s number,
Therefore,
The friction factor will be equal to,
Therefore, according to the below equation
According to the above result, the Reynolds’s number will be
To find the flow rate,
The flow in pipe 1 is considered as the flow away from the junction
Similarly for pipe 2,
To find the Reynolds’s number,
The roughness ratio for pipe 2 will be,
To find Reynolds’s number,
Try
Therefore,
The friction factor will be equal to,
Therefore, according to the below equation
According to above result, the Reynolds’s number will be
To find the flow rate,
The flow in pipe 2 is considered as the flow towards the junction.
For pipe 3,
Therefore,
Hence
Try
Therefore,
The friction factor will be the same.
According to the above result, the Reynolds’s number will be
To find the flow rate,
The flow in pipe 1 is considered as flow away from the junction
Similarly for pipe 2,
To find Reynolds’s number,
Therefore,
Friction factor will be the same.
Therefore, according to the below equation
According to the above result, the Reynolds’s number will be
To find the flow rate,
The flow in pipe 2 is considered as the flow towards the junction.
Similarly for pipe 3,
To find Reynolds’s number,
Try
Therefore,
The roughness ratio for pipe 3 will be,
The friction factor will be equal to,
According to the above result, the Reynolds’s number will be
To find the flow rate,
The flow in pipe 3 is considered as the flow towards the junction.
Therefore the flow rate will be,
By further iteration, we can get this close to zero, but for now, according to the obtained results, we can say,
Conclusion:
The flow rates in each pipe is equal to,
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Chapter 6 Solutions
Fluid Mechanics
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