1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Work performed by a compressor

  1. Mar 7, 2014 #1
    1. The problem statement, all variables and given/known data

    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?

    2. Relevant 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

    3. 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?
  2. jcsd
  3. Mar 8, 2014 #2
    ##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: Mar 8, 2014
  4. Mar 8, 2014 #3
    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.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted