A fluid of density
(a)
The expression for the average pressure at the inlet and the throat in terms of the given variables without any irreversibility.
Answer to Problem 62P
The average pressure at inlet is
The average pressure at throat is
Explanation of Solution
Given information:
The cross sectional area at inlet is
Write the expression for conservation of mass equation for section (1) and section (2).
Here, the mass flow rate at inlet is
Write the equation for mass flow rate through inlet
Write the equation for mass flow rate through throat.
Write the expression for conservation of mass for section (1) and section (3).
Here, the mass flow rate at the outlet is
Write the equation for mass flow rate through throat
Calculation:
Substitute
Substitute
Write the Bernoulli's equation for section (1) and (3).
Substitute
Write the expression for Bernoulli's equation for section (2) and (3).
Substitute
Conclusion:
The average pressure at the throat is
(b)
Whether the actual pressure at the inlet is higher or lower than the prediction.
Answer to Problem 62P
The pressure at the inlet in real flow is higher than the predicted value.
Explanation of Solution
Write the expression for the Bernoulli's equation for section (1) and section (3) including frictional losses.
Here, the frictional loss is
Substitute
Conclusion:
The actual pressure at the inlet is higher than the predicted value of the pressure at inlet.
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Chapter 5 Solutions
Fluid Mechanics: Fundamentals and Applications
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