---
title: "Vertical standpipe wall thickness"
subject: "Strength of Materials"
chapter: 5
key: "semester_3/strength_of_materials:standpipe-wall-thickness"
source: https://www.bctengineer.com/q/semester_3/strength_of_materials/standpipe-wall-thickness
site: BCT Engineering
---

# Vertical standpipe wall thickness

Strength of Materials · Chapter 5: Thin Walled Vessels

- Asked in: 2080 Baisakh, 4 marks
- Video: [Thin Pressure vessel 08 | Hoop Stress |and Axial stress in Vertical Pipe](https://www.youtube.com/watch?v=qAMfuWGom74) — Sunil Mohod
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/strength_of_materials/standpipe-wall-thickness
- Whole chapter: https://www.bctengineer.com/md/semester_3/strength_of_materials/chapter-5

## Question

A vertical thin walled standpipe is 4 m in diameter and stands 30 m high. If the allowable working stress in tension is $120\ \text{N/mm}^2$, what is the required wall thickness of the pipe?

## Short answer

Water pressure at base ρgh=0.2943 N/mm². Required thickness from hoop stress formula t=pd/(2σ_allow)=0.2943×4000/(2×120)=4.91 mm, provide about 5 mm.

## Answer

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).**

## Check yourself

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

1. Where is the pressure greatest and how is it calculated?
   A. At the base, p = rho g h = 0.2943 N/mm2
   B. At the top, p = rho g h
   C. At mid height, p = rho g h / 2
   D. At the base, p = rho g d
   Answer: A. Hydrostatic pressure increases with depth, so the base governs. (Key point: Pressure used)

2. Why is the hoop stress used to find thickness?
   A. It is half the longitudinal stress
   B. It is twice the longitudinal stress, so it governs
   C. Longitudinal stress is zero in a standpipe
   D. It is independent of pressure
   Answer: B. sigma_c = pd/2t is larger than sigma_l = pd/4t. (Key point: Governing stress)

3. Which relation gives the thickness?
   A. t = pd/(4 sigma) = 2.45 mm
   B. t = pd/sigma = 9.81 mm
   C. t = pd/(2 sigma) = 4.91 mm
   D. t = p/(2 sigma d) = 0
   Answer: C. 0.2943 x 4000 / 240 = 4.91 mm. (Key point: Thickness)

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