
The velocity of the nitrogen at the pipe’s inlet and outlet.

Explanation of Solution
Given:
The initial pressure
The initial temperature
The final pressure
The final temperature
Calculation:
Write the formula for mass flow rate of nitrogen gas at initial and final.
Write the formula for mass flow rate of nitrogen gas at initial and final.
Here, the cross sectional area of the pipe is
Here, the inlet and exit mass flow rates are equal and the diameter of the pipe is constant
Equate the Equations (I) and (II) to obtain the exit velocity
Refer Table A-2E (a), “Ideal-gas specific heats of various common gases”.
The specific heat of nitrogen gas is
Substitute
Consider the nitrogen gas flows at steady state through one inlet and one exit system (pipe and duct flow). Hence, the inlet and exit mass flow rates are equal.
Write the energy rate balance equation for one inlet and one outlet system.
Here, the rate of heat transfer is
The nitrogen gas flows at steady state through the system. Hence, the rate of change in net energy of the system becomes zero.
Neglect the heat transfer (adiabatic process), work transfer and potential energy changes i.e.
The Equations (I) reduced as follows.
The change in enthalpy is expresses as follow.
Here, the specific heat is
Substitute
Substitute
Thus, the velocity of the nitrogen at the pipe’s inlet is
Substitute
Thus, the velocity of the nitrogen at the pipe outlet is
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Chapter 6 Solutions
Fundamentals of Thermal-Fluid Sciences
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