Vertical standpipe wall thickness

A standpipe is a vertical pipe filled with water. The pressure is greatest at the base, so the wall must be thickest there; the hoop stress governs because it is twice the longitudinal stress.

Data: $d = 4$ m $= 4000$ mm, $h = 30$ m, $\sigma_{allow} = 120\ \text{N/mm}^2$, $\rho_w = 1000\ \text{kg/m}^3$, $g = 9.81\ \text{m/s}^2$.

Water pressure at the base

$$p = \rho g h = 1000(9.81)(30) = 294\,300\ \text{N/m}^2 = 0.2943\ \text{N/mm}^2$$

Thickness (hoop stress)

$$\sigma_c = \frac{pd}{2t} \Rightarrow t = \frac{pd}{2\sigma_c} = \frac{0.2943\times4000}{2\times120} = 4.91\ \text{mm}$$

Answer: required thickness $\approx 4.91\ \text{mm}$; provide about 5 mm (the thickness could be reduced higher up where the pressure is less).