Work performed by a compressor

1. Mar 7, 2014

Fluidman117

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. Mar 8, 2014

Sunfire

$P=\dot{m}\Delta h$ - 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
3. Mar 8, 2014

Staff: Mentor

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