(a)
The volume flow rate of water through the pipe.
(a)
Answer to Problem 136EP
The volume flow rate through the circular pipe is
Explanation of Solution
Given information:
The length of the pipe is
Write the given expression for velocity distribution in circular pipe for fully developed laminar flow.
Write the general expression for velocity distribution in circular pipe for fully developed laminar flow.
Here maximum velocity is
Write the expression for average velocity for fully developed laminar flow in circular pipe.
Here average velocity is
Write the equation for volume flow rate.
Here volume flow rate is
Calculation:
Below figure shows the velocity profile in a fully developed flow in a circular pipe.
Figure-(1)
Compare Equation (I) with Equation (II)
Substitute
Substitute
Conclusion:
The volume flow rate through the circular pipe is
(b)
The pressure drop across the pipe.
(b)
Answer to Problem 136EP
The pressure drop is
Explanation of Solution
Given information:
The length of the pipe is
Write the given expression for velocity distribution in circular pipe for fully developed laminar flow.
Write the general expression for velocity distribution in circular pipe for fully developed laminar flow.
Here maximum velocity is
Write the expression for average velocity for fully developed laminar flow in circular pipe.
Here average velocity is
Write the equation for volume flow rate.
Here volume flow rate is
Write the expression for pressure drop in a fully developed laminar flow in circular pipe.
Here pressure drop is
Calculation:
Below figure shows the velocity profile in a fully developed flow in a circular pipe.
Figure-(1)
Compare Equation (I) with Equation (II)
Substitute
Substitute
Substitute
Conclusion:
The pressure drop is
(c)
The pumping power required to drive the fluid.
(c)
Answer to Problem 136EP
The pumping power required is
Explanation of Solution
Given information:
The length of the pipe is
Write the given expression for velocity distribution in circular pipe for fully developed laminar flow.
Write the general expression for velocity distribution in circular pipe for fully developed laminar flow.
Here maximum velocity is
Write the expression for average velocity for fully developed laminar flow in circular pipe.
Here average velocity is
Write the equation for volume flow rate.
Here volume flow rate is
Write the expression for pressure drop in a fully developed laminar flow in circular pipe.
Here pressure drop is
Write the expression for pumping power required to drive the fluid.
Calculation:
Below figure shows the velocity profile in a fully developed flow in a circular pipe.
Compare Equation (I) with Equation (II)
Substitute
Substitute
Substitute
Substitute
Conclusion:
The pumping power required is
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Chapter 8 Solutions
Fluid Mechanics Fundamentals And Applications
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