Concept explainers
Repeat Prob. 14-55E, ignoring all minor losses. How important are the minor losses in this problem? Discuss.
Whether the minor losses are important or not.
Answer to Problem 57EP
The minor losses are important because the volume flow rate is increased by
Explanation of Solution
Given Information:
Inner diameter of the duct is
Expression for steady energy equation from point 1 in the stagnant air region to point 2 at the duct outlet.
Here, the required head for the fan is
Expression for the total head loss.
Here, the velocity of the air is
Expression for Reynolds's number.
Here, the kinematic viscosity is
Expression for relative roughness.
Here, the roughness of the pipe is
Expression for the friction factor.
Expression for the volume flow rate.
Here, the area of the pipe is
Expression for the area of the pipe.
Substitute
.
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
Expression for the total head loss.
Here, the velocity of the air is
Calculation:
Refer to the Table-A-9E, "Properties of air at 1 atm pressure" to obtain the density of the air as
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Since at the operating point the available head and the required head are equal, therefore equate Equation (XIII) and (XIV).
Solve Equation (XIII) and Equation (XV) to obtain the value of velocity as
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Since at the operating point the available head and the required head are equal, therefore equate equation (XVI) and (XVIII).
Solve Equation (XVII) and Equation (XIX) to obtain the value of velocity as
Substitute
Therefore, the volume flow rate when considering the minor losses is
Conclusion:
The minor losses are important because the volume flow rate is increased by
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Chapter 14 Solutions
Fluid Mechanics: Fundamentals and Applications
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