Thermodynamics: Compressor Axial work

[FreelandME]

Homework Statement

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Thermodynamics problem

Air enters a compressor at a temperature of 290 Kelvin and pressure 100 kPa with a stable volume flow of 2.5 m^3/s. The output temperature of the compressor is is 400 Kelvin and the velocity of the flow is 30 m/s. Air is implied to be an ideal gas under those conditions. The cooling of the compressed is done with a refrigant that absorbs heat from the air with a speed of 750 kJ / min. If the changes in kinetic and dynamic energies are negligible and the flow is permanent then find the axial force needed for the compressor to work .

Could someone help me with this problem? I'd really appreciate it , at least some help where i shoudl start from

Homework Equations

The Attempt at a Solution

I'm having trouble where to start from , first thoughts where to find the state of air through the tables in the input and output of compressor , but beside that i haven't come to a better idea yet

 

[Chestermiller]

Let me guess. You're learning about the (open system) flow version of the first law of thermodynamics, correct? If so, please write down the relevant equation that applies to this situation. You are going to need to determine the outlet pressure. Based on the first sentence in the problem statement, what it the mass flow rate? If you want to find the axial force on the rotor, you are going to need to do a momentum balance also. How would you express that?

Chet

 

[FreelandME]

Q₁₂ - W ₁₂ = m [ h₂ - h₁ + (V₂²- V₂¹)/2+ g (z₂-z₁)] (1)

and since

we have kinetic and dynamic energies neglible
Q₁₂ = 0
E(mass in-mass out) = 0 aswell

so we take from 1

W₁₂= h₂ - h₁

after working out a bit with it that's what i finished to , i find enthalpies from tables with linear intepollaration , but is this the axial work of compressor or I'm mistaken?

 

[Chestermiller]

Q is not zero. So

Q - W = m(h₂-h₁)

Do you know how to determine the mass flow rate, given the information in the first sentence of the problem statement?

Chet

 

[FreelandME]

I'm pretty sure we use the ideal gas law to find the density and then with multiplication of density with the volume flow rate we find the mass flow rate, now some questions as Q we use the heat that the refrigant absorbs so Q=-750KJ/min , the W we finally get is the axial work I am looking for? Where should i use the velocity flow at that is given on the second sentence?

 

[Chestermiller]

I'm pretty sure we use the ideal gas law to find the density and then with multiplication of density with the volume flow rate we find the mass flow rate, now some questions as Q we use the heat that the refrigant absorbs so Q=-750KJ/min , the W we finally get is the axial work I am looking for?

Yes.

Where should i use the velocity flow at that is given on the second sentence?

Well, you are also asked to find the force on the rotor. This is where the velocity of flow would come in. So, a momentum balance would be involved. But I've been having trouble with this because there seems to be a piece of vital information missing (according to my judgement). I feel that, to do the momentum balance, you need to know either the inlet velocity or the cross sectional area of the compressor. The information at the outlet end seems adequate, when combined with the mass flow rate at the inlet end. Has anything been left out in the problem statement regarding the inlet or the cross sectional area?

Chet

 

[FreelandME]

Nothing has been left out

 

[Chestermiller]

Nothing has been left out

Well, anyway, please try writing out algebraically a momentum balance on the gas, taking the entire compressor as the control volume and letting F be the force that the rotor exerts horizontally on the gas.