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rySAFETY VALVE CAPACITY DETERMINATION FOR LIQUIDS
The expression for the mass of liquid, wf, kg/hr, flowing through a safety valve of seat aera A, mm2, is;
(1)
w_1=36\cdot A\cdot c_f\cdot \sqrt{2\cdot p\cdot sg}\;\;\;\;\;\;\;\;\;\;(kg/hr)
where
p
= flowing pressure in bar gauge
sg
= specific gravity of liquid (relative to 1 for water)
cf
= coefficient of discharge of valve seat (may depend upon value of flowing pressure)
wf
= mass flow of liquid in kg/hr
do
= safety valve seat bore in mm
vf
= volumetric flow of liquid in litres/min
pt
= safety valve relieving set pressure
If do = valve seat diameter in mm, (1) becomes
(2)
w_f=40\cdot d^{2}_{o}\cdot c_f\cdot \sqrt{p\cdot sg}\;\;\;\;\;\;\;\;\;\;(kg/hr)
Expressed in flowing liquid volume vf, litres/min,
v_f=\frac{40}{60}\cdot d^{2}_{o}\cdot c_f\cdot \sqrt{\frac{p}{sg}}\;\;\;\;\;\;\;\;\;\;(litres/min)
(3)
=0.667\cdot d^{2}_{o}\cdot c_f\cdot \sqrt{\frac{p}{sg}}\;\;\;\;\;\;\;\;\;\;(litres/min)
The coefficient of discharge is often found to be dependant upon the pressure accumulation above set pressure pt. Two levels of accumulation are envisaged in BS 6759 part 3, 10% and 25%. If the respective coefficients of discharge are denoted cf10 and cf25, (2) & (3) become;
(2a)
w_f=40\cdot d^{2}_{o}\cdot c_{f10}\cdot \sqrt{1.1p_t\cdot sg}\;\;\;\;\;\;\;\;\;\;(kg/hr)
and
(2b)
w_f=40\cdot d^{2}_{o}\cdot c_{f25}\cdot \sqrt{1.25p_t\cdot sg}\;\;\;\;\;\;\;\;\;\;(kg/hr)
also
(3a)
v_f=0.677\cdot d^{2}_{o}\cdot c_{f10}\cdot \sqrt{\frac{1.1p_t}{sg}}\;\;\;\;\;\;\;\;\;\;(litres/min)
and
(3b)
v_f=0.677\cdot d^{2}_{o}\cdot c_{f25}\cdot \sqrt{\frac{1.25p_t}{sg}}\;\;\;\;\;\;\;\;\;\;(litres/min)
Conveniently, the expessions (2b) and (3b) may be transposed to determine the minimum safety valve seat diameters for a required flow at a given set pressure;
(4)
d_o\geq\sqrt{\frac{0.025\cdot w_f}{c_{f25}\cdot \sqrt{1.25p_t\cdot sg}}}\;\;\;\;\;\;\;\;\;\;(mm)\;\;\;\;\;\geq\sqrt{\frac{0.2236\cdot w_f}{c_{f25}\cdot \sqrt{p_t\cdot sg}}}\;\;\;\;\;\;\;\;\;\;(mm)
and
(5)
d_o\geq\sqrt{\frac{1.50\cdot v_f\cdot \sqrt{sg}}{c_{f25}\cdot\sqrt{1.25p_t}}}\;\;\;\;\;\;\;\;\;\;(mm)\;\;\;\;\;\geq\sqrt{\frac{1.3416\cdot v_f\cdot \sqrt{sg}}{c_{f25}\cdot\sqrt{p_t}}}\;\;\;\;\;\;\;\;\;\;(mm)
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