Thermo problem (for TFS and HVACR test takers)

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Slay the P.E.

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Happy Monday!

Take a stab at this one. Show your work :)  

SPOILER ALERT: Try to solve it first; then scroll down to see the replies.

throttle and mass conservation.PNG

 
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A = 2" ?

RHO1*A1*V1 = RHO2*A2*V2

RHO = 1/SPECIFIC VOLUME

SOLVE FOR A2 = (RHO1/RHO2) * A1* (V1/V2 =4) (edit: this should have been =.1/4 not 4)

SOLVING FOR A2 ALLOWS FOR D2

I get 1.933"

 
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I come up with (B)

I solved for the downstream quality and the computed the specific volume, using the quality.  Then used v2/a2 = 4 * v1/a1 and solved for a2.  Then computed diameter from a2.   I came up with diameter d2 = 3.85 in.

On a side note:  NEVER use a solenoid as an expansion device.  You will wire draw the valve.

 
Last edited by a moderator:
I come up with (B)

I solved for the downstream quality and the computed the specific volume, using the quality.  Then used v2/a2 = 4 * v1/a1 and solved for a2.  Then computed diameter from a2.   I came up with diameter d2 = 3.85 in.
Nicely done. Quality should be about 0.179.

On a side note:  NEVER use a solenoid as an expansion device.  You will wire draw the valve.
10-4.

 
I come up with (B)

I solved for the downstream quality and the computed the specific volume, using the quality.  Then used v2/a2 = 4 * v1/a1 and solved for a2.  Then computed diameter from a2.   I came up with diameter d2 = 3.85 in.

On a side note:  NEVER use a solenoid as an expansion device.  You will wire draw the valve.
How did you come up with v2/a2 = 4v1/a1?

I did come up with d2=[(34.48 d1^2 / 4(0.58)]^1/2 = 3.855in

This is pretty similar to that NCEES problem, but here it is assumed that the vapor had the same velocity with the fluid at the downstream.

 
How did you come up with v2/a2 = 4v1/a1?
Conservation of mass flow and velocity constraint.   m1=m2,   rho1 A1 V1= rho2 A2 V2   and    V2 = 4*V1...  Combine and simplify.   V= velocity   v=specific volume= 1/rho

 
Last edited by a moderator:
Conservation of mass flow and velocity constraint.   m1=m2,   rho1 A1 V1= rho2 A2 V2   and    V2 = 4*V1...  Combine and simplify.   V= velocity   v=specific volume= 1/rho
Oh yes same, did not notice the small v being specific volume. 

 
side question: Would you be able to determine the velocity of this problem using the Bernoulli equation?

 
No. The Bernoulli equation is derived for incompressible fluids (constant density). Here you have a considerable change in density due to the phase change.

 

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