1. Identify if the condition is critical or not critical by calculating the Cv required for critical pressure drop
F superheat=627.8F (difference in temperature from saturated steam)
k=1+(0.0007*F superheat)
m=9254 lb/hr
Pi=800.6 psia
Cv=9.5
Cv=mk/(1.82*Pi)
Cv=9.142
Valve Cv > Critical Cv,
Thus
Case 1 would be non-critical pressure drop.
Now to calculate pressure drop use the equation for non critical pressure drops
Cv = mk / (2.1 ( (pi + po)*(p1-p2))^1/2)
((Pi+Po)(Pi-Po))^1/2)=mk/2.1Cv
(Pi^2-Po^2)=(mk/2.1Cv)^2
Po^2=Pi^2-(mk/2.1Cv)^2
Po^2= 195127
Po=441.7 psi
dP=800.6-441.7= 358.9=>359 psi
assume ideal gas
density @ inlet conditions = 14.06 kg/m^3
volumetric flowrate=0.08293m^3/s=2.93ft^3/s
P1V1=P2V2
V2=P1V1/P2
V2=5.31 cubic fps
bore=19mm=0.75 in
cross sectional area=0.44 in^2=0.003056 ft^2
velocity = 5.31 ft^3/s /0.003056f ft^2
final velocity = 1737.6 fps
calculate temperature of final steam stream, too lazy to look up steam tables
Link
Ti=1112F
Tf=546F
sonic velocity @ outlet conditions aka critical velocity = 1804 fps
mach ratio = 1738/1804=0.963
You can use this link to calculate dBA, but considering its pretty close to Mach 1, its going to be loud af.
Link
Do the same as above for problem 2.