Question

Air is compressed from 12 psia and 77.3◦F to a pressure of 145 psia while being cooled at a rate of 15 Btu/lbm by circulating water through the compressor casing. The volume flow rate of the air at the inlet conditions is 6000 ft3 /min, and the power input to the compressor is 800 hp. Determine (a) the mass flow rate of the air and (b) the temperature at the compressor exit

Answer 1

a)mass flow=6lbm/s

b)the temperature at the compressor exit= 1269◦F

Step-by-step explanation:

Hello!

To solve this problem we will perform the following steps

1.Use thermodynamic tables to find the density and entalpy of the air using the properties of temperature and pressure (2 psia and 77.3 ° F)

Density = 0.06032 lbm / ft ^ 3

h1=entalpy=351.2Btu/lbm

2.

Calculate the mass flow by multiplying the flow by the density, remember to apply conversion factors

`m=0.06032(lbm)/(ft^3) 6000(ft^3)/(min) (1min)/(60s)=6lbm/s`

3.We apply first law of thermodynamics in the compressor, it establishes that the energy that enters a system is the same that must come out.

Energies entering the compressor =

-Electric power (800hp)

=W=565.65btu/s

-flow energy (mh1)

energies coming out of the compressor

-heath= (Q)(m

)

-flow energy (mh2)

applying the above we have the following energy balance equation

W+mh1=Qm+mh2

Our goal is to determine the value of the enthalpy of output h2 in order to find the air temperature using thermodynamic tables

`(W+mh1-Qm)/(m)=h2\\(565.65+(6)(351.2)-(15)(6))/(6) =h2\\ h2=430.46Btu/lbm`

4.finally we use thermodynamic tables to find the temperature using enthalpy

T2=1269◦F