Concept explainers
(a)
The rate of flow of oil through the funnel when diameter of pipe is doubled.
The funnel effectiveness when the diameter of the pipe is doubled.
Answer to Problem 83P
The rate of flow through the funnel is
The funnel effectiveness is
Explanation of Solution
Given information:
The temperature of oil is
Write the expression for the flow rate in the tunnel.
Here, the pipe length is
The exit point is taken as reference level.
Write the expression for the energy equation.
Here, the inlet pressure is
The exit is taken as the reference level; there is no turbine or pump, the flow is frictionless, the correction factor of kinetic energy is unity and the head loss is zero.
The fluid is open to atmosphere at inlet and outlet.
Write the expression for the maximum flow rate.
Write the expression for the funnel effectiveness.
Here, the given flow rate is
Calculation:
Substitute
Therefore, the rate through the funnel is
Substitute
Substitute
Substitute
Substitute
Substitute
Therefore, the funnel effectiveness is
Conclusion:
Therefore, the rate of flow through the funnel is
Therefore, the funnel effectiveness is
(b)
The rate of flow of oil via the funnel when the length of pipe is tripled and diameter is maintained the same.
The funnel effectiveness when the length of pipe is tripled and diameter is maintained the same.
Answer to Problem 83P
The rate of flow through the funnel is
The funnel effectiveness is
Explanation of Solution
Given information:
The temperature of oil is
Write the expression for the flow rate in the tunnel.
Here, the pipe length is
The exit point is taken as reference level.
Write the expression for the energy equation.
Here, the inlet pressure is
The exit is taken as the reference level; there is no turbine or pump, the flow is frictionless, the correction factor of kinetic energy is unity and the head loss is zero.
The fluid is open to atmosphere at inlet and outlet.
Write the expression for the maximum flow rate.
Write the expression for the funnel effectiveness.
Here, the given flow rate is
Calculation:
Substitute
Therefore, the flow rate through the funnel is
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The rate of flow through the funnel is
The funnel effectiveness is
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Chapter 8 Solutions
Fluid Mechanics: Fundamentals and Applications
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