For the duct system and fan of Prob. 14-55E, partially closing the damper would decrease the flow rate. AU else being unchanged, estimate the minor loss coefficient of the damper required to decrease the volume flow rate by a factor of 2.
The minor loss coefficient of the damper.
Answer to Problem 56EP
The minor loss coefficient of the damper is
Explanation of Solution
Given information:
Inner diameter of the duct is
Expression for the required head using the energy balance equation.
Here, the initial pressure is
Expression for the capacity.
Expression for the available head
Here, the shutoff head is
Substitute
Expression for the Reynolds number
Here, the velocity of the water is
Expression for the roughness factor
Here, the diameter of the pipe is
Expression for the minor losses
Here, the minor loss coefficient at pipe entrance is
Expression for the total head loss
Here, the friction factor is
Expression for the friction factor using the Colebrook equation
Expression to convert the shutoff head from inches of water column to inches of air column
Here, the density of the water is
Expression to convert the
Calculation:
Refer to the Table-A-9E, "Properties of air at
Substitute
Substitute
Substitute
Refer to Figure A-12 "Moody chart" to obtain the friction factor as
Substitute
Substitute
Here, the exit is equal to the total velocity of the water.
Substitute
Let us consider that the air is flowing through the duct turbulent at
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The minor loss coefficient of the damper is
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