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Work performed by a compressor

  • #1

Homework Statement



Nitrogen was compressed from initial pressure of 101 kPa to a higher pressure. The respective enthalpies are: 54 kJ/kg and 350 kJ/kg. The compression process is adiabatic and ideal. The volume flow rate is 0.05 m^3/s. Density of Nitrogen before entering the compressor is 1.1 kg/m3 and at high pressure it is 35 kg/m3.

Calculate the work performed by the compressor?

Homework Equations



W = m_dot * (h2-h1);

m_dot - mass flow rate in kg/s
h1 = 54 kJ/kg
h2 = 350 kJ/kg

m_dot = Q*rho
Q = 0.05 m^3/s

The Attempt at a Solution



It is easy to plug in the numbers and calculate it, but I am a bit confused about the mass flow rate. When calculating the mass flow rate, do I have use the density at lower pressure or higher pressure and why?
 

Answers and Replies

  • #2
221
4
##P=\dot{m}\Delta h## - That would be the power of the compressor, its units are [J/s]
To calculate work, you'll need to integrate the power over time. Probably they want you to calculate the work done on compressing 1 kg of nitrogen. That's where you'll need both densities, to estimate how long does the compressor take to raise the density of 1kg nitrogen. Once you have the time interval, then

##Work=\dot{m}\Delta h \Delta t##
 
Last edited:
  • #3
20,231
4,264

Homework Statement



Nitrogen was compressed from initial pressure of 101 kPa to a higher pressure. The respective enthalpies are: 54 kJ/kg and 350 kJ/kg. The compression process is adiabatic and ideal. The volume flow rate is 0.05 m^3/s. Density of Nitrogen before entering the compressor is 1.1 kg/m3 and at high pressure it is 35 kg/m3.

Calculate the work performed by the compressor?

Homework Equations



W = m_dot * (h2-h1);

m_dot - mass flow rate in kg/s
h1 = 54 kJ/kg
h2 = 350 kJ/kg

m_dot = Q*rho
Q = 0.05 m^3/s

The Attempt at a Solution



It is easy to plug in the numbers and calculate it, but I am a bit confused about the mass flow rate. When calculating the mass flow rate, do I have use the density at lower pressure or higher pressure and why?
You've definitely done this calculation correctly. I think the volumetric flow rate corresponds to the exit of the compressor. If it was the inlet, the mass flow rate would only be 0.05 kg/sec (=3 kg/min) which sounds awfully low for any practical application. On the other hand, 105 kg/min is more like it.

Chet
 

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