Question

Air enters an adiabatic compressor through 0:5m2 opening and exhausts through a 0:2m2 opening. The inlet conditions of air are 200 kPa and 52C with an unknown velocity and exits at 3 MPa and 427C with a velocity of 100 m/s. Determine the mass ow rate of air through the compressor, the inlet velocity and the power required to run the compressor.

Answer 1

Answer:

i) 43.55 kg/s

ii) 40 m/s

iii)  -199.32 KW

Explanation:

To resolve the above question we have to make some assumptions :

• mass flow  through the system is constant
• The only interactions that are between the system and the surrounding are work and heat
• The fluid is uniform

i) first we have to determine the mass flow rate of the air

M = $(\frac{P1}{RT1} )A1v1$

    = $( \frac{200}{0.287*325} ) 0.5 * V1$ ---------- (1) hence  M = 43.55 kg/s

ii) using this relationship : A1V1 = A2V2 hence V1 = (0.2/0.5) * 100 = 40m/s (    inlet velocity )

input this value into equation 1

iii) Next we will determine the power required to run compressor

attached below

power required = -199.32 KW ( this value indicates that there is power supplied )