---
title: "Penstock plate thickness (1.5 m, 250 m head)"
subject: "Hydro Power"
chapter: 5
key: "semester_6/hydro_power:penstock-thickness-1-5m"
source: https://www.bctengineer.com/q/semester_6/hydro_power/penstock-thickness-1-5m
site: BCT Engineering
---

# Penstock plate thickness (1.5 m, 250 m head)

Hydro Power · Chapter 5: Components of Hydropower System

- Asked in: 2082 Chaitra, 5 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/hydro_power/penstock-thickness-1-5m
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-5

## Question

A steel penstock pipe has an internal diameter of 1.5 m. It is designed to carry water under a pressure head of 250 m. Considering a 30% allowance for pressure rise due to water hammer, determine the required thickness of the pipe plate. Use a design stress of 120 N/mm² and a joint efficiency of 85%.

## Short answer

Design pressure p = 1.30 × 250 m × 9810 N/m³ = 3.188 N/mm². Thickness t = pD/(2 σ η_j) = (3.188 × 1500)/(2 × 120 × 0.85) = 23.44 mm, so use 24 mm.

## Answer

**Given:** $D = 1.5$ m $= 1500$ mm, static head $H = 250$ m, water hammer allowance 30%, design stress $\sigma = 120$ N/mm², joint efficiency $\eta_j = 0.85$.

**Formula** (thin cylinder, hoop stress):

$$
t = \frac{p\,D}{2\,\sigma\,\eta_j}
$$

#### Design pressure
$$
\begin{aligned}
H_d &= 1.30 \times 250 = 325\ \text{m} \\
p &= \gamma_w H_d = 9810 \times 325 = 3.188 \times 10^6\ \text{N/m}^2 \\
&= 3.188\ \text{N/mm}^2
\end{aligned}
$$

#### Thickness
$$
\begin{aligned}
t &= \frac{3.188 \times 1500}{2 \times 120 \times 0.85} \\
&= \frac{4782.4}{204} = 23.44\ \text{mm}
\end{aligned}
$$

**Answer:** required plate thickness $t = 23.44$ mm, say **24 mm** (adding a corrosion allowance of about 2 mm, a 26 mm plate would be used in practice).

## Check yourself

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

1. What design head is used for the 250 m static head with 30% water hammer?
   A. 325 m
   B. 250 m
   C. 280 m
   D. 75 m
   Answer: A. 1.30 x 250 = 325 m. (Key point: Water hammer allowance)

2. The design pressure in N/mm^2 is about
   A. 31.9
   B. 3.19
   C. 0.319
   D. 325
   Answer: B. p = 9810 x 325 = 3.188 x 10^6 N/m^2 = 3.188 N/mm^2. (Key point: Pressure units)

3. Which formula gives the required thickness?
   A. t = p D / (sigma eta_j)
   B. t = p sigma / (2 D eta_j)
   C. t = p D / (2 sigma eta_j)
   D. t = 2 p D eta_j / sigma
   Answer: C. Hoop stress in a thin cylinder with joint efficiency. (Key point: Formula)

4. The required thickness (before corrosion allowance) is about
   A. 11.7 mm
   B. 46.9 mm
   C. 2.34 mm
   D. 23.4 mm
   Answer: D. t = 3.188 x 1500 / (2 x 120 x 0.85) = 23.44 mm. (Key point: Result)

## Related in Hydro Power

- [Water hammer in 250 m penstock](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Awater-hammer-250m-penstock) — Hydro Power, chapter 1
- [Penstock thickness (1.3 m, 20 kg/cm²)](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Apenstock-thickness-1-3m) — Hydro Power, chapter 5
- [Water hammer in elastic cast-iron pipe](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Awater-hammer-cast-iron-pipe) — Hydro Power, chapter 1
- [Penstock thickness (1.20 m, 17.5 kg/cm²)](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Apenstock-thickness-1-2m) — Hydro Power, chapter 5
- [Water hammer in 200 mm pipe](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Awater-hammer-200mm-pipe) — Hydro Power, chapter 1
- [Penstock thickness and economic diameter](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Apenstock-thickness-economic-diameter) — Hydro Power, chapter 5

## Related in other subjects

- [Water hammer in 1.2 m steel pipe, wall thickness](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Awater-hammer-steel-pipe-thickness-1200mm) — Hydraulics, chapter 4
- [Water pipe thickness from pressure head](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Awater-pipe-thickness-pressure-head) — Strength of Materials, chapter 5
- [Economic diameter; penstock thickness (1.25 m)](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Apenstock-economic-diameter-thickness-1-25m) — Hydropower Engineering, chapter 6
- [Economic diameter factors; penstock wall thickness (3 m)](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Aeconomic-diameter-and-wall-thickness-factors) — Hydropower Engineering, chapter 6