August 24, 2019

# Modeling Relief Valve (Pressure Safety Valve) Thrust force

Start-Prof can estimate the support loads and stresses caused by relief valve discharge by static method.

The relief valve discharge thrust load acts on elbow 28. In Start-Prof it should be applied at the end of the elbow in 29 node.

There’s a two methods to estimate the dynamic equivalent thrust force F:

• ASME B31.1 method
• Direct calculation of V1 и P1 by special software like Hydrosystem

## ASME B31.1 Method

Equivalent dynamic thrust force can be estimated by equation:
F = DLF ∙ F1
where
DLF – dynamic load factor, depend on first natural period of piping. If period is unknown the DLF=2.0.

F1 – static reaction force, kgf. May be computed by the following equation:

where
W – mass flow rate (relieving capacity stamped on the valve by 1.11), kg/sec
gc=9.81 m/sec² – gravitational constant,
Pa – atmospheric pressure, kgf/sm²
A1 – exit flow area, sm²  A1=p(D-2t)²/4
V1 – exit velocity (node  36), m/sec

P1 – static pressure, kgf/sm²

h0 – stagnation enthalpy at the safety valve inletMJ/kg
J = 101970.408 m*kgf/MJ
a, b – constants according to table below

 Steam Condition a, MJ/kg b Wet steam <90% quality 0.6769 11 Saturated steam ≥90%  quality 1.05 kgf/sm² ≤ P1 ≤ 70.31 kgf/sm² 1.9143 4.33 Superheated steam ≥90%  quality 0.07 kgf/sm² ≤ P1 ≤ 140.61 kgf/sm² 1.93291 4.33

### Example

Example project file: ReliefValve.ctp. See how to open the piping model file

Input data:

• Diameter of discharge pipe: 21.9 sm

• Wall thickness of discharge pipe: 1.6 sm

• product: Saturated steam

• relief valve relieving capacity: 48 kg/sec

• Steam pressure: 64 kgf/sm²

• Steam temperature: 538°C

Calculation:

A1=p(D-2t)²/4 = 3.14159(21.9-2∙1.6)²/4 = 274.65 sm²
a = 1,9143 MJ/kg
b = 4.33
W = 48∙1.11 = 53.28 kg/sec
stagnation enthalpy for steam at 70 kgf/sm² and 538°C h0 =  3,506 MJ/kg
P1=53.28/274.65*(4.33-1)/4.33*(2*(3.506-1.9143)*101970.408/(2*4.33-1)/9.81)^0.5 = 9.8 kgf/sm²
V(2*9.81*101970.408*(3.506-1.9143)/(2*4.33-1))^0.5 = 644.77 m/sec
F1 = 53.28*644.77/9.81 + (9.8-1)*274.65 = 5919 kgf
F = DLF ∙ F1 = 2*5919 = 11838 kgf