Thermo problem (for TFS and HVACR test takers)

[Slay the P.E.]

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.

 

[ME_VT_PE]

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"

 

[MikeGlass1969]

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.

 

[Slay the P.E.]

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.

 

[Vel2018]

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.

 

[MikeGlass1969]

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

 

[Vel2018]

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. 

 

[mongolianbbq]

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

 

[Slay the P.E.]

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