### Sample Problem Statement

Design a 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/m^{3}

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,

A : orifice are requirement in mm^{2}

Q : flowrate in lit/min

Q = 100000×1000/(1000×60) = 1666.67 lit/min

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

P_{1} : upstream pressure in kPag

P_{1} = 500 kPag

P_{2} : downstream pressure in kPag

P_{2} = 50 kPag

K_{d} : Coefficient of discharge

K_{d} = 0.65 for liquid service

K_{W} : correction factor

K_{W} = 1 (for conventional relief valves with near atmospheric backpressure)

K_{C} : combination correction factor for use of rupture discs

K_{C} = 1 (for absence of rupture disc upstream to the valve)

K_{ν} : correction factor due to viscosity

K_{ν} = 1 (calculated using following equations from API 520 Part I)

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

A = 14.17 cm^{2}

### 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 cm^{2} 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.