Concept explainers
he pressure at the location when velocity of air and sound are equal.
The temperature at the location when velocity of air and sound are equal.
The ratio of the areas to entrance area.
Answer to Problem 41EP
The pressure at the location when velocity of air and sound are equal to each other is
The temperature at the location when velocity of air and sound are equal to each other is
The ratio of the areas to entrance area is
Explanation of Solution
Given information:
The initial pressure of the air is
Write the expression for the stagnation temperature.
Here, the initial temperature is
Write the expression for the stagnation pressure.
Here, the initial pressure is
Write the expression for the pressure ratio.
Here, the pressure at exit is
Write the expression for the temperature ratio.
Here, the temperature at exit is
Write the expression for the Mach number at inlet.
Here, the velocity of the sound is
Write the expression for the velocity of sound.
Substitute
Write the expression for the ratio of area.
Here, the area at inlet is
Calculation:
Consider the air as an ideal gas. Therefore, the list of properties for the ideal gas at room temperature is
The specific heat ratio is
The gas constant is
The specific heat at constant pressure is
Substitute
Substitute
Since, the velocity of the air is equal to the velocity of sound hence the value of Mach number is 1.
Refer to table “One dimensional isentropic compressible flow function for the an ideal gas” to obtain the pressure ratio as
Substitute
Substitute
Substitute
Substitute
Conclusion:
The pressure at the location when velocity of air and sound are equal is
The temperature at the location when velocity of air and sound are equal is
The ratio of the areas to entrance area is
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Chapter 12 Solutions
FLUID MECHANICS:FUND.+APPL.(LL)>CUSTOM<
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