Question 16.3: A safety valve of diameter 50 mm is to blow off at a gange p...
A safety valve of diameter 50 mm is to blow off at a gange pressure of 0.5 MPa. It is held by a close coiled compression spring of average diameter 70 mm and the initial compression of the spring is 20 mm. Determine the diameter of the spring wire and the number of turns if the allowable shear stress is 190 MPa and the shear modulus is 80 GPa
Force required to lift the valve
=p\times\frac{\pi}{4}d^2_v=0.5\times\frac{\pi}{4}\times50^2=981.75 NUsing Eq. (16.1) (neglecting d/4R if 4R >>d)
\tau =\frac{16PR}{\pi d^3} \left\lgroup1+\frac{d}{4R} \right\rgroup (16.1)
\tau =\frac{16PR}{\pi d^3}or, 190=\frac{16\times981.75\times35}{\pi d^3}
or, d = 9.73 say 10 mm
Number of coils are given by Eq. (16.2),
\delta =\frac{64nPR^3}{Gd^3} (16.2)
n=\frac{\delta Gd^4}{64PR^3}=\frac{20\times80000\times10^4}{64\times981.75\times35^3} =5.94 say 6 turns
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