Answer to Question #214574 in Mechanical Engineering for Nano

Question #214574

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 pmax = 2.23 MPa. If the free height (i.e., uncompressed height) of the spring hfree = 135 mm and its spring stiffness k = 5 kN/m, what should be the dimension h of the valve?


1
Expert's answer
2021-07-08T04:02:03-0400

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


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