determine the dimensions of the tanka conical

Question

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/mm², determine the dimensions of the tank.

Solution

Unit weight of water, w = 9.81 × 10^{- 3} N/mm³.

Apex angle, α = 15^o

Thickness, t = 10 mm

Permissible tensile stress, σ_n = 140 N/mm²

Therefore, we get 140 = wh²  tan α / 4t cos α

=9.81 × 10^{- 3} × h² 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.