Carbon dioxide enters an adiabatic nozzle at 1200 K with a velocity of 50 m/s sand leaves at 400 K. Assuming constant specific heats at room temperature, determine the Mach number (a) at the inlet and (b) at the exit of the nozzle. Assess the accuracy of the constant specific heat approximation.
(a)
The Mach at the inlet of the nozzle.
Answer to Problem 63P
The Mach at the inlet of the nozzle is
Explanation of Solution
Given information:
The nozzle is adiabatic, the inlet temperature carbon dioxide at inlet is
Write the expression for the speed of sound.
Here, the gas constant is
Write the expression for the Mach number.
Here the velocity of the flow is
Calculation:
Refer to the table A1, "molar mass gas constant and ideal gas specific heat of some substances" to obtain the gas constant for carbon dioxide as
Refer to the table A1, "molar mass gas constant and ideal gas specific heat of some substances" to obtain the specific heat ratio for carbon dioxide as
Substitute
Substitute
Conclusion:
The Mach at the inlet of the nozzle is
(b)
The Mach at the exit of the nozzle.
Answer to Problem 63P
The Mach at the exit of the nozzle is
Explanation of Solution
Write the expression for the energy balance Equation applied at inlet and exit of the nozzle.
Here, the velocity at inlet is
Write the expression for the enthalpy at inlet.
Here, the specific heat at constant pressure is
Write the expression for the enthalpy at Outlet.
Here, the specific heat at constant pressure is
Substitute
Calculation:
Refer to the table A1 "molar mass gas constant and ideal gas specific heat of some substances" to obtain the specific heat for constant pressure for carbon dioxide as
Substitute
Substitute
Substitute
Conclusion:
The Mach at the exit of the nozzle is
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Chapter 2 Solutions
Fluid Mechanics Fundamentals And Applications
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