---
title: "Water hammer in 250 m penstock"
subject: "Hydro Power"
chapter: 1
key: "semester_6/hydro_power:water-hammer-250m-penstock"
source: https://www.bctengineer.com/q/semester_6/hydro_power/water-hammer-250m-penstock
site: BCT Engineering
---

# Water hammer in 250 m penstock

Hydro Power · Chapter 1: Introduction to Basic Fluid Mechanics and Hydraulics

- Asked in: 2082 Kartik, 2+2 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/hydro_power/water-hammer-250m-penstock
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-1

## Question

Water flows through a 250 m long penstock pipe at a velocity of 2.5 m/s. If the pipe is suddenly closed, determine the pressure rise due to water hammer and the period of oscillation of the pressure wave, assuming a wave speed of 1,450 m/s.

## Short answer

Pressure rise calculated by Joukowsky equation Δp = ρcV = 3.625 MPa (369.5 m head). Period of oscillation T = 4L/c = 0.69 s for L=250 m, c=1450 m/s.

## Answer

Sudden closure means the valve closes in less than $2L/c$, so the full Joukowsky pressure rise occurs.

#### Pressure rise
$$
\begin{aligned}
\Delta p &= \rho c V = 1000 \times 1450 \times 2.5 = 3.625 \times 10^6\ \text{N/m}^2 = 3.625\ \text{MPa} \\
\Delta H &= \frac{cV}{g} = \frac{1450 \times 2.5}{9.81} = 369.5\ \text{m of water}
\end{aligned}
$$

#### Period of oscillation
The pressure wave travels to the reservoir and back twice in one full cycle (high pressure phase + low pressure phase):
$$
\begin{aligned}
T &= \frac{4L}{c} = \frac{4 \times 250}{1450} = 0.690\ \text{s}
\end{aligned}
$$
(The time for one round trip, $2L/c = 0.345$ s, is the critical closure time.)

**Answer:** Pressure rise = 3.625 MN/m² (≈ 369.5 m head); period of oscillation = 0.69 s.

## Check yourself

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

1. When is the full Joukowsky pressure rise developed?
   A. When closure time is greater than 2L/c
   B. When the valve is closed in less than 2L/c
   C. Only when the pipe is flexible
   D. Only when velocity is below 1 m/s
   Answer: B. If closure is faster than the round trip time 2L/c, the reflected wave has not returned and the full rise rho c V occurs. (Key point: Sudden closure)

2. What is the pressure rise for c = 1450 m/s and V = 2.5 m/s?
   A. 3.625 MPa
   B. 0.369 MPa
   C. 36.25 MPa
   D. 1.45 MPa
   Answer: A. Delta p = rho c V = 1000 x 1450 x 2.5 = 3.625 x 10^6 N/m^2, about 369.5 m of water. (Key point: Pressure rise)

3. What is the period of oscillation of the pressure wave?
   A. T = L/c
   B. T = 2L/c
   C. T = 4L/c = 0.69 s
   D. T = c/L
   Answer: C. One full cycle needs four pipe-length trips: T = 4L/c = 4 x 250/1450 = 0.69 s. (Key point: Period)

## Related in Hydro Power

- [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
- [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 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
- [Pressure rise for gradual and sudden closure](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Awater-hammer-valve-closure) — Hydro Power, chapter 1
- [Water hammer effects and gradual closure](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Awater-hammer-gradual-closure) — 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

## Related in other subjects

- [One cycle of water hammer pressure wave](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Awater-hammer-one-cycle-wave-sketch) — Hydraulics, chapter 4, asked 2×
- [Penstock pressure rise and pressure-time sketch](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Asurge-tank-penstock-pressure-rise) — Hydraulics, chapter 4
- [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
- [Pressure rise: rigid versus elastic pipe](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Arigid-vs-elastic-pipe-pressure-rise-5km) — Hydraulics, chapter 4