Question

A compressor receives air at 290 K, 100 kPa and a shaft work of 5.5 kW from a gasoline engine. It is to deliver a mass flow rate of 0.01 kg/s air to a pipeline. Assuming a constant-pressure specific heat of Cp = 1.004 kJ/kg-K for the air, determine the maximum possible exit pressure of the compressor

Answer 1

Answer:

$P_2=4091\ KPa$

Explanation:

Given that

T₁ = 290 K

P₁ = 100 KPa

Power P =5.5 KW

mass flow rate

$\dot{m}= 0.01\ kg/s$

Lets take the exit temperature = T₂

We know that

$P=\dot{m}\ C_p (T_2-T_1)$

$5.5=0.01\times 1.005(T_2-290})\\T_2=\dfrac{5.5}{0.01\times 1.005}+290\ K\\\\T_2=837.26\ K$

If we assume that process inside the compressor is adiabatic then we can say that

$\dfrac{T_2}{T_1}=\left(\dfrac{P_2}{P_1}\right)^{0.285}$

$\dfrac{837.26}{290}=\left(\dfrac{P_2}{100}\right)^{0.285}\\2.88=\left(\dfrac{P_2}{100}\right)^{0.285}$

$2.88^{\frac{1}{0.285}}=\dfrac{P_2}{100}$

$P_2=40.91\times 100 \ KPa$

$P_2=4091\ KPa$

That is why the exit pressure will be 4091 KPa.