Calculating pressure at pressure relief valve outlet

[smims]

I have a tank which has a Pressure Relief Valve (PRV) connected to the atmospheric vent (Carbon steel with friction coefficient of 0.14). The PRV is opened at Set pressure of 30 PSIG and has a capacity of 60,000 SATSTM (I assumed it to be in lb/hr). I am trying to calculate the discharge pressure at the vent exit (opening).

The steps,

1. From steam table, specific volume of dry saturated steam at 30 PSIG = 9.5 cu.ft./lb
2. Calculating the volume flow rate at the exit = 60,000 x 9.5 = 570,000 cu.ft./hr = 158.33 cu.ft./sec
3. Calculating the nozzle outlet cross sectional area = 0.55 sq.ft. (Pipe nozzle diameter = 10 in = 0.83 ft)
4. Velocity at the exit = 158.33 x 0.55 = 290 ft/sec
5. Calculating pressure drop = (Friction coefficient/2) x (Pipe Length/Pipe Diameter) x (Velocity squared/gravity) = 0.14 x (10 ft /0.83 ft) x (290.35x290.35/32.17) = 2201 ft = 953 psi (Impossible!)

here is the excel file http://www.filedropper.com/prv_1

If I include the density in the above pressure drop calculation, the unit turns out to be in PSI than ft. But then I found no such equation that includes the density in calculating the pressure drop. What am I missing? Thanks.

 

[Nidum]

Pressure at the outlet of the vent pipe will be equal to atmospheric pressure - 0 psig .

 

[OldYat47]

If you are working this as an exercise then Nidum can be considered close enough. If this is a real relief valve application you are better (and much safer) relying on a reliable supplier to do the calculation for you. Pressure at the outlet nozzle can be well above atmospheric pressure because a pressurized area will form at the outlet under actual relief.

 

[smims]

I used a large Friction coefficient (3.5E-06 is the right one).
The pressure turned out to be 0.15 PSIG. So Nidum is right.

Thanks for your comments.

 

[JChemP]

It's worth noting that it is possible for the pressure at your vent outlet to be higher than atmospheric pressure if you have critical flow. i.e mach 1 conditions at vent outlet. For the vent pressure drop you need to use the density at downstream pressure which will be be the backpressure created during relief which will less than the set pressure. It seems you have used the upstream density for your pressure drop calcs. First you need to check if the flow is critical at the vent outlet. If not your pressure at the outlet will be atmospheric. If it is then your pressure drop will be higher than atmospheric. Then you need to back calculate the pressure back to the relief valve outlet.