Determine the dimensions of the tank:
A conical water tank is to be fabricated from steel plate of 10 mm thickness. The shell should contain an apex angle (α) 15o. If the permissible tensile stress is 140 N/mm^{2}, determine the dimensions of the tank.
Solution
Unit weight of water, w = 9.81 × 10^{- 3} N/mm^{3}.
Apex angle, α = 15^{o}
Thickness, t = 10 mm
Permissible tensile stress, σ_{n }= 140 N/mm^{2}
Therefore, we get 140 = wh^{2 } tan α / 4t cos α
=9.81 × 10^{- 3} × h^{2} tan 15^{o} / 4 × 0 × cos 15^{o}
∴ h = 1434.5 mm
We know, r = h tan α = 1434.5 tan 15^{o} = 384.4 mm. Base radius = 384.4 mm.