The steady flow rates in each pipe.
Answer to Problem 6.121P
Explanation of Solution
Given information:
Diameter of all pipes are
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 all pipes will be,
To find Reynolds’s number,
Therefore,
The friction factor will be equal to,
Therefore, according to below equation
According to 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,
Try
Therefore,
The friction factor will be same.
According to above result, the Reynolds’s number will be
To find the flow rate,
The flow in pipe 2 is considered as flow towards the junction.
For pipe 3,
Therefore,
Hence
Try
Therefore,
The friction factor will be same.
According to 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,
The friction factor will be same.
According to above result, the Reynolds’s number will be
To find the flow rate,
The flow in pipe 2 is considered as flow towards the junction.
Similarly for pipe 3,
To find Reynolds’s number,
Try
Therefore,
The friction factor will be equal to,
According to above result, the Reynolds’s number will be
To find the flow rate,
The flow in pipe 3 is considered as 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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