---
title: "Water pipe thickness from pressure head"
subject: "Strength of Materials"
chapter: 5
key: "semester_3/strength_of_materials:water-pipe-thickness-pressure-head"
source: https://www.bctengineer.com/q/semester_3/strength_of_materials/water-pipe-thickness-pressure-head
site: BCT Engineering
---

# Water pipe thickness from pressure head

Strength of Materials · Chapter 5: Thin Walled Vessels

- Asked in: 2073 Shrawan, 8 marks
- Video: [Pipe Wall Thickness: Pressure Analysis](https://www.youtube.com/watch?v=xs55pbZoXbc) — Kenneth Lamb
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/strength_of_materials/water-pipe-thickness-pressure-head
- Whole chapter: https://www.bctengineer.com/md/semester_3/strength_of_materials/chapter-5

## Question

A water pipe 500 mm internal diameter contains water at a pressure head 100 m. If the unit weight of water is $10\ \text{KN/m}^3$ and allowable stress of pipe material is $20\ \text{N/mm}^2$. Calculate the thickness of the pipe.

## Short answer

Water pressure p = γh = 1 N/mm². Using hoop stress σ = pd/(2t), required thickness t = (1×500)/(2×20) = 12.5 mm (practically 13 mm).

## Answer

**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).**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How is the pipe pressure obtained from a 100 m head?
   A. p = unit weight x head = 10 x 100 = 1000 kN/m^2 = 1 N/mm^2
   B. p = 100 N/mm^2
   C. p = 10 N/mm^2
   D. p = 1000 N/mm^2
   Answer: A. 1000 kN/m^2 equals 1 N/mm^2 because 1 m^2 = 10^6 mm^2. (Key point: Pressure from head)

2. Which stress is used to design the thickness, and why?
   A. Longitudinal stress, because it is smaller
   B. Hoop stress, because it is twice the longitudinal stress
   C. Shear stress pd/8t
   D. Radial stress, because it acts on the pipe wall
   Answer: B. Hoop stress is the larger, so t from sigma_c = pd/2t satisfies both. (Key point: Governing stress)

3. What thickness results?
   A. 25 mm
   B. 6.25 mm
   C. 12.5 mm
   D. 10 mm
   Answer: C. t = pd/(2 sigma) = 1 x 500/(2 x 20) = 12.5 mm. (Key point: Thickness)

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