Solution Found!
Energy Analysis of Control Volumes at Steady
Chapter 4, Problem 57P(choose chapter or problem)
At steady state, a well-insulated compressor takes in nitrogen at \(60^{\circ} \mathrm{F}, 14.2 \mathrm{lbf} / \mathrm{in}^2\), with a volumetric flow rate of \(1200 \mathrm{ft}^3 / \mathrm{min}\). Compressed nitrogen exits at \(500^{\circ} \mathrm{F}, 120 \mathrm{lbf} / \mathrm{in}^2\) Kinetic and potential energy changes from inlet to exit can be neglected. Determine the compressor power, in hp, and the volumetric flow rate at the exit, in \(\mathrm{ft}^3 / \mathrm{min}\).
Questions & Answers
QUESTION:
At steady state, a well-insulated compressor takes in nitrogen at \(60^{\circ} \mathrm{F}, 14.2 \mathrm{lbf} / \mathrm{in}^2\), with a volumetric flow rate of \(1200 \mathrm{ft}^3 / \mathrm{min}\). Compressed nitrogen exits at \(500^{\circ} \mathrm{F}, 120 \mathrm{lbf} / \mathrm{in}^2\) Kinetic and potential energy changes from inlet to exit can be neglected. Determine the compressor power, in hp, and the volumetric flow rate at the exit, in \(\mathrm{ft}^3 / \mathrm{min}\).
ANSWER:Step 1 of 2
We have to determine the compressor power and the volumetric flow rate at the exit for a well insulated compressor.
The compressor power can be determined by using the steady state energy rate balance
equation
Now, the control volume is at steady state that is, 0 and the kinetic energy and potential energy from inlet to exit can be can be neglected ,so the last two terms is equal to zero.
Hence,
Where,
compressor power in hp
mass flow rate in lb/h
and
are the enthalpy of the nitrogen at the inlet and
exit of the compressor in Btu/lb
The mass flow rate can be found using the expression,
From ideal gas equation of state
Now, 14.2 lb/in2 ,
ft3/min ,
60 oF = 520 oR
and M = molecular weight of nitrogen = 28.01
So,
Thus, with Btu/lb and
6693.1 Btu/min for N2 gas at T1= 60 oF and T2= 500 oF from Table A-23 E
