Temperature and pressure change in a diffuser

[Laura Morrison]

I am totally stuck on this question. It is about a diffuser and it does not tell you what fluid is running through the system.

 

"A diffuser has the following inlet conditions:

 

p1=100kPa

T1=300K

Velocity=200m/s

Area=100m²

Specific Volume=1.6445m³/kg

 

The exit velocity is 20m/s

 

Calculate the exit pressure, temperature and the mass flow rate. (Assume adiabatic operation)."

 

Would it be correct to use the Bernoulli equation, taking into account enthalpy and kinetic energy changes, to calculate the exit pressure? This is assuming density is constant.

 

I am not aware of any equation which will allow me to work out the exit temperature without knowing what substance is actually contained in the system.

 

Any help with this would be very much appreciated,

Thanks

Edited December 6, 2013 by Laura Morrison

[studiot]

What you require is known as the steady flow energy equation.

 

This considers both the total mass and the energy within the system to be constant

 

However what you have is homework and needs to be in the homework section.

 

You did state your thoughts at starting and the SFEE is a formalised equation combining Bernoulli and thermodynamics, so

 

U₁ + P₁V₁ + KE₁ +PE₁ + Q = U₂+ P₂V₂ + KE₂ +PE₂+ W

 

This can be developed to set some of these quantities to zero, given your conditions, and using specific (per mass) quantities, to solve your problem.

 

You will also need the mass continuity equation.

 

There's lots about it on the net, but come back to discuss your problem further if you wish.

 

https://www.google.co.uk/#q=steady-flow+energy+equation

 

the Manchester article is very good and probably similar to the approach in your college.

Edited December 6, 2013 by studiot

[Enthalpy]

Your gas is not air: too light. At 15.2g/mol it's nearly methane, not ammonia nor neon - so it must be a mix.

 

The exit temperature does need the exact Cp.

 

If you knew the Cp (or Cv, or gamma, or atoms per stiff molecule):

Kinetic energy converts into enthalpy, in adiabatic operation. Near 1bar 300K, gasses are perfect so you deduce the temperature rise from the enthalpy change, then deduce the rest from the temperature ratio. The step through temperature is nearly always the best.

 

But this particular case does not need the exact Cp to get the exit pressure. You can keep the Cp as a parameter:

- Deduce the temperature rise as a function of Cp. The rise is inversely proportional to Cp.

- Write the pressure ratio as a function of the temperature ratio.

- Observe that the relative temperature variation is small in your case, even for a monoatomic gas

- So you can linearize the P variation versus T variation.

- This linearized form is proportional to Cp, so both influences cancel out, and you don't need the Cp.

 

The mass throughput is obvious at the inlet.