The steady flow rates in each pipe and the difference in both the results.
Answer to Problem 6.122P
The flow rates found in this part is 5.2 times lower than that of part P6.121. It is because the flow rate is dependent on the cross-sectional area. Therefore, reducing the diameter from 28 to 15 will decrease the amount of flow rate.
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 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 flow away from the junction
Similarly for pipe 2,
To find Reynolds’s number,
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 2 is considered as 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,
The friction factor will be same.
According to the 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,
In part P6.121, the flow rate were,
Therefore, we can say,
The flow rates found in this part is 5.2 times lower than that of part P6.121. It’s because the flow rate is dependent on the cross-sectional area. Therefore, reducing the diameter from 28 to 15 will decrease the amount of flow rate.
Conclusion:
The flow rates in each pipe is equal to,
The flow rates are 5.2 times lower than that of part P6.121.
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Chapter 6 Solutions
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