Concept explainers
Water to a residential area is transported at a rate of 1.5
In order to reduce pumping power requirements, it is proposed to line the interior surfaces of the concrete pipe with 2-cm-thick petroleum-based lining that has a surface roughness thickness of 0.04 mm. There is a concern that the reduction of pipe diameter to 66 cm and the increase in average velocity may offset any gains. Taking
The increase or decrease of percent in the pumping power requirements due to pipe frictional losses as a result of lining concrete pipes.
Answer to Problem 82P
The percent decrease in the pumping power requirements is
Explanation of Solution
Given information:
The volume flow rate is
Write the expression for the cross-sectional area of pipe without coating.
Here, the internal diameter of the pipe is
Write the expression for the average velocity of flow in the pipe.
Here, the volume flow rate of water is
Write the expression for finding the Reynolds number.
Here, the kinematic viscosity is
Write the expression for the Colebrook relation of the friction factor for turbulent flow.
Here, the friction factor is
Write the expression for the head loss in the pipe1.
Here, the length of the pipe is
Write the expression for the new diameter of the pipe with the lining.
Here, the thickness of the pipe is
Write the expression for the new cross-sectional area of the pipe.
Here, the new diameter of the pipe with the lining is
Write the expression for the new average velocity.
Here, the new cross-sectional area of the pipe is
Write the expression for finding the Reynolds number.
Here, the new average velocity is
Write the expression for the new friction function from the Colebrook relation.
Here, the Reynolds number is
Write the expression for finding the new head loss.
Write the expression for the percentage reduction.
Here, the new head loss is
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The percent decrease in the pumping power requirements is
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Chapter 8 Solutions
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