Wednesday, October 22, 2008

TE 303 - HW #5, P1 - Adiabatic Steam Nozzle - 10 pts

Steam at 3 MPa and 400oC enters an adiabatic nozzle at a velocity of 40 m/s and leaves at 2.5 MPa and 300 m/s. Determine…

a.) The temperature of the steam when it leaves the nozzle.

b.) The ratio of the inlet cross-sectional area to the outlet cross-sectional area, A1 / A2.

Assume the process operates at steady-state.

No old comments.

7 comments:

Anonymous said...

I am confused here. I come up with the formula deltaH + dv^2/(2g) = 0. So solving, H2 = -dv^2/(2g)+H2, yet this gives me a negative number because the deltaKE is so large (but negative). You can't have negative enthalpy, right? Continuing, even if I rearrange (probably incorrectly) and get a positive number, should I get T2 out of this interpolating from the table, or using dH=CpdT?

Anonymous said...

Also, to find the cross sectional areas don't we need a mass flow rate? mdot=(vavg*Across)/(specific volume)

Anonymous said...

HINTS:

* You can find T2 from H2 using ThermalFluids (or other steam tables). Think about what the phase of the material will be when it is leaving the nozzle.

* Remember that at steady state, the mass flow rate is constant! You can use this knowledge and the definition of the mass flow rate to calculate A1/A2.


ANSWERS:
H2: 3187.5 kJ/kg

T2: (around 400 C) -- you determine the exact value

A1/A2 = 6.42

Anonymous said...

Dear anonymous,

Please let me know if the hints that I just posted don't help you figure out your problem.

Dr. B said...

Anonymous 8:32 AM:
I am just guessing, but I think you have a UNITS problem. I think you want H in kJ/kg and I suspect that when you calculated Ekin you actually had units of J/kg.

I hope this helps.

Dr. B said...

Anonymous 8:34 AM:
You cannot really determine EITHER A1 or A2, but you can determine the RATIO. When you setup the ratio, the mass flow rate will cancel because Mdot1 = Mdot2 at steady-state!

Best of luck.

Anonymous said...

I just worked with some students through IM, and we realized that they were thinking of "dv^2" incorrectly. This term means d(v^2) or (v2^2 - v1^2) and NOT (dv)^2. Remember that KE is one which is not path dependent, so we can write KEfinal - KEinitial, which would give us (v2^2 - v1^2)/2m.