The volume that flows in each duct and the cross-section size of the longer duct.
Answer to Problem 6.114P
The flow rate in small duct is equal to
The flow rate in long duct is equal to
The cross-section size of long duct is equal to
Explanation of Solution
Given information:
The length of the small duct is
The length of the longer duct is
The plenum pressure is equal to
The volume flow rate in the longer duct is three times that of small duct.
The energy equation for this problem can be written as,
In the above equation,
The Reynolds’s number is defined as,
Calculation:
Assume,
Calculate the hydraulic diameter of the duct,
For a square duct,
Hydraulic diameter = Side length of the duct
Therefore,
Assume,
According to the energy equation,
Calculate Reynolds’s number
Calculate the roughness ratio
Calculate the exact value of friction factor
Not a considerable amount of change in friction factor, therefore take
Therefore,
Calculate the flow rate in small duct,
To find the flow rate in longer duct,
We know that,
To find the cross-section size of longer duct,
We need to find the hydraulic diameter of the longer duct.
Therefore, rewrite the energy equation for longer duct,
Assume
Calculate the velocity of the flow
Calculate the Reynolds’s number
Calculate the roughness ratio
Calculate the exact value of friction factor
Therefore, according to the new friction factor, find the exact value of the cross-section size
Conclusion:
The flow rate in small duct is equal to
The flow rate in long duct is equal to
The cross-section size of long duct is equal to
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Chapter 6 Solutions
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