---
title: "Penstock thickness (1.3 m, 20 kg/cm²)"
subject: "Hydro Power"
chapter: 5
key: "semester_6/hydro_power:penstock-thickness-1-3m"
source: https://www.bctengineer.com/q/semester_6/hydro_power/penstock-thickness-1-3m
site: BCT Engineering
---

# Penstock thickness (1.3 m, 20 kg/cm²)

Hydro Power · Chapter 5: Components of Hydropower System

- Asked in: 2082 Kartik, 4 marks
- Video: [Penstock Pipe Numerical || Hydropower Engineering](https://www.youtube.com/watch?v=N97FrIIFTr8) — OPengineer
- 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-1-3m
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-5

## Question

Calculate the thickness of a penstock pipe with an internal diameter of 1.3 m that conveys water under a pressure head of 20 kg/cm², considering a 20% potential increase in pressure due to water hammer. Use a design stress of 1050 kg/cm² and a joint efficiency of 90%.

## Short answer

Design pressure p = 1.20 × 20 = 24 kg/cm². Thickness t = pD/(2 σ η_j) = (24 × 130)/(2 × 1050 × 0.90) = 1.651 cm = 16.51 mm, so use 17 mm.

## Answer

**Given:** $D = 1.3$ m $= 130$ cm, pressure $p_0 = 20$ kg/cm², water hammer rise 20%, design stress $\sigma = 1050$ kg/cm², joint efficiency $\eta_j = 0.90$.

**Formula** (hoop stress in a thin pipe):

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

#### Design pressure
$$
p = 1.20 \times 20 = 24\ \text{kg/cm}^2
$$

#### Thickness
$$
\begin{aligned}
t &= \frac{24 \times 130}{2 \times 1050 \times 0.90} \\
&= \frac{3120}{1890} = 1.651\ \text{cm} = 16.51\ \text{mm}
\end{aligned}
$$

**Answer:** penstock thickness $t = 16.5$ mm, say **17 mm** (plus about 2 mm corrosion allowance if required).

## Check yourself

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

1. With 20 kg/cm^2 and 20% water hammer, the design pressure is
   A. 24 kg/cm^2
   B. 20 kg/cm^2
   C. 4 kg/cm^2
   D. 40 kg/cm^2
   Answer: A. 1.20 x 20 = 24. (Key point: Design pressure)

2. Why is D taken as 130 cm?
   A. Because the thickness must be in metres
   B. Pressure and stress are in kg/cm^2, so D must be in cm
   C. Because joint efficiency is in cm
   D. It is a mistake; 1.3 m should be used
   Answer: B. Units must be consistent: kg/cm^2 with cm gives t in cm. (Key point: Unit consistency)

3. What is the effect of joint efficiency in the formula?
   A. It multiplies the thickness, so a lower value gives a thinner plate
   B. It has no effect on thickness
   C. It sits in the denominator, so a lower efficiency gives a thicker plate
   D. It replaces the design stress
   Answer: C. t = pD/(2 sigma eta_j). (Key point: Joint efficiency)

4. The thickness obtained is
   A. 8.3 mm
   B. 33 mm
   C. 1.65 mm
   D. 16.5 mm, say 17 mm
   Answer: D. t = 24 x 130 / (2 x 1050 x 0.9) = 1.651 cm. (Key point: Result)

## Related in Hydro Power

- [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
- [Penstock plate thickness (1.5 m, 250 m head)](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Apenstock-thickness-1-5m) — Hydro Power, chapter 5
- [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
- [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
- [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

- [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
- [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
- [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
- [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