# Pressure Relief Valve Sizing Calculations â€“ Blocked Liquid Discharge

### Sample Problem Statement

Design aÂ  pressure relief valve for the following service.

Protected equipment : Separator vessel
Relief service : Water
Reason for relief : Blocked liquid discharge
Relieving Rate : 100,000 kg/hr
Water Density : 1000 kg/m3
Water Viscosity : 0.8 cP
Set pressure : 5 barg
Accumulation : 10%
Back pressure at relief valve discharge : 0.5 barg
Type of relief valve : Conventional

### Solution

This sample problem for relief valve sizing calculation can be solved in following steps, which are based on pressure relief valve sizing procedures described in API RP 520 Part I.

### Step1

As per API RP 520 Part I, the required orifice area for relief valve discharge is calculated using the following equation,

... (1)

A : orifice are requirement in mm2

Q : flowrate in lit/min
Q = 100000Ã—1000/(1000Ã—60) = 1666.67 lit/min

G : Specific gravity of the liquid = 1 (for water)

P1 : upstream pressure in kPag
P1 = 500 kPag

P2 : downstream pressure in kPag
P2 = 50 kPag

Kd : Coefficient of discharge
Kd = 0.65 for liquid service

KW : correction factor
KW = 1 (for conventional relief valves with near atmospheric backpressure)

KC : combination correction factor for use of rupture discs
KC = 1 (for absence of rupture disc upstream to the valve)

KÎ½ : correction factor due to viscosity
KÎ½ = 1 (calculated using following equations from API 520 Part I)

and

Plugging this data into equation (1), the minimum required orifice area for the relief valve is calculated to be,
A = 14.17 cm2

### Step2

The next higher available orifice area should be selected for the pressure relief valve to be actually installed. Referring to the table of standard orifice sizes given in EnggCyclopedia's relief valve sizing calculator,

Next high available orifice area is selected to be A = 18.49 cm2 and the corresponding designating letter is 'L'. Available valve sizes are '3L4' and '4L6', which correspond to different nozzle sizes for suction and discharge nozzles of the pressure relief valves. For a '3L4' valve suction nozzle is of 3" size and discharge nozzle of 4" size. Similarly for a '4L6' valve suction nozzle is 4" and discharge is of 6" size.