Question

A safety valve (pressure relieve valve) on top of a pressure vessel containing steam under pressure p = 2 MPa, has a discharge hole of diameter d = 10 mm as shown in the figure below. The valve is designed to release the steam when the pressure reaches the maximum allowable value p_max = 2.23 MPa. If the free height (i.e., uncompressed height) of the spring h_free = 135 mm and its spring stiffness k = 5 kN/m, what should be the dimension h of the valve?

Answer 1

$F= pk(L-h)= \frac{\pi p_{max}d^2}{4}\\ h= L-\frac{\pi p_{max}d^2}{4k}\\ h= \frac{135}{1000}-\frac{\pi *2.23*(\frac{10}{1000})^2}{4*5}\\ h= \frac{135}{1000}-0.00003502876 = 0.13496 m$