Concept explainers
The initial discharge rate of water via the pipe.
The time taken to empty the swimming pool.
The value of the friction factor.
Whether the minor loss is really minor or not.
Answer to Problem 155P
The discharge rate of water via the pipe is
The time taken to empty the swimming pool is
The given value of the friction factor is not accurate and the reasonable value of friction factor is
The value of minor loss is truly minor.
Explanation of Solution
Given information:
The swimming pool diameter is
The flow is incompressible and turbulent. The difference in elevation between the fountain and the pipe is null. The pressure at the inlet ad the exit is atmospheric in nature.
Write the expression to calculate the energy equation. Assume the effect of kinetic energy correction factor to be negligible.
Here, the inlet pressure is
Write the expression to calculate the exit velocity when time is
Here, he volume flow rate is
Write the expression for the area of cross section.
Here, the diameter of the pipe is
Substitute
Write the expression to calculate the head loss.
Here, the diameter of the pipe is
Write the expression for the elevation at any given time.
Here, the coefficient of minor loss is
Write the expression for the flow rate at any time given.
Substitute
Write the expression to calculate the water amount flowing b=via the pipe for a differential time.
Here, the differential time is
Substitute
Write the expression for the area of the tank.
Here, the diameter of the tank is
Write the expression for the decrease of volume of water in the swimming pool.
Here, the negative change in datum of tank is
Substitute
Integrate Equation (XIII) from
Write the expression to calculate the Reynolds number.
Here, the viscosity of the fluid is
Write the expression for the Colebrook equation.
Here, the friction factor is
Calculation:
Refer to Table A-3, "Properties of saturated water" to obtain the value of
The flow is fully developed making the roughness of the plastic null.
Substitute
Substitute
Consider the time is zero.
Substitute
Substitute
Convert
Substitute
Substitute
Substitute
Substitute
Hence, the value of the minor loss is truly minor as the friction factor remains unchanged.
Conclusion:
The discharge rate of water via the pipe is
The time taken to empty the swimming pool is
The given value of the friction factor is not accurate and the reasonable value of friction factor is
The value of minor loss is truly minor.
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Chapter 8 Solutions
Fluid Mechanics: Fundamentals and Applications
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