Water pipe thickness from pressure head

Data: internal diameter $d = 500$ mm, pressure head $h = 100$ m of water, $\gamma_w = 10\ \text{kN/m}^3$, allowable stress $\sigma = 20\ \text{N/mm}^2$.

Pressure in the pipe

$$p = \gamma_w h = 10\ \text{kN/m}^3\times100\ \text{m} = 1000\ \text{kN/m}^2 = 1\ \text{N/mm}^2$$

Thickness

The hoop stress is the larger stress, so it governs the design:

$$\sigma_c = \frac{pd}{2t} \Rightarrow t = \frac{pd}{2\sigma_c} = \frac{1\times500}{2\times20} = 12.50\ \text{mm}$$

Check of the longitudinal stress: $\sigma_l = \dfrac{pd}{4t} = 10.0\ \text{N/mm}^2 < 20$, safe.

Answer: thickness $t = 12.5\ \text{mm}$ (provide 13 mm or more in practice).