Concept explainers
The coefficient of discharge of the orifice.
Answer to Problem 152P
The coefficient of discharge is
Explanation of Solution
Given information:
The diameter of tank 1 is
Assume the free surface for tank as
Write the expression to calculate the energy equation for the system.
Here, the pressure in tank is
The surface of the tank is open to atmosphere.
Here, the atmospheric pressure is
Write the expression for the pressure in orifice.
Here, the fluid height in tank 2 is
Write the expression for the net fluid height in the system.
Here, the height in tank 1 is
Write the Equation (II) in derivative form.
Here, the fluid height in tank is
Write the expression for the volume flow rate through the orifice.
Here, the coefficient of discharge is
Write the expression for the volume flow through orifice in terms of time derivatives.
Here, the area of tank 2 is
Write the expression for the area of tank 1.
Here, the diameter of tank 1 is
Write the expression for the area of tank 2.
Here, the diameter of tank 2is
Write the expression for the area of orifice.
Here, the diameter of orifice is
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Integrate Equation (VIII) with limits
Substitute
Substitute
Conclusion:
The coefficient of discharge is
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Chapter 8 Solutions
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