Air, modeled as an ideal gas, is compresses at steady state from 1 bar, 300 K, to 5 bar, 500K, with 150 kW of power input. Heat transfer occurs at a rate of 20 kW fom the air to cooling water circulating in a water jacket enclosing the compressor. Neglecting kinetic energy and potential energy effects, determine the mass flow rate of the air, in kg/s.

0.64 Kg/s

Explanation:

Given

-Fluid: Air

-Inlet 1:

Pressure P1 = 1 bar

Temperature T2 = 300 K

-Exit 2:

Pressure P2 = 5 bar

Temperature T2 = 500 K

-Power input to compressor W = - 150 KW

-The rate of heat transfer from the air to cooling water circulating in a water jacket enclosing the compressor Q = - 20 KW

Required:

-Mass flow rate m [kg/s]

Assumption:

-Constant average values

-Steady flow

-Kinetic energy effects are ignored

-Potential energy effects are ignored

-Ideal gas.

Solution:

Energy equation could be defined by.

Q - W=m[ (h2-h1) + (V_2^2-V_1^2/2) + g (Z_2-Z_1) ]

As kinetic and potential energy are ignored.

Q - W=m (h2-h1)

Specific enthalpy for air at P1 = 1 bar and T2 = 300 K from table

h1 = 300.1 KJ/Kg

Specific enthalpy for air at P2 = 5 bar and T2 = 500 K from table

h2 = 503.2 KJ/Kg

The mass flow rate could be calculated as following.

m = Q - W / (h2-h1)

= 0.64 Kg/s