---
title: "Water hammer in elastic cast-iron pipe"
subject: "Hydro Power"
chapter: 1
key: "semester_6/hydro_power:water-hammer-cast-iron-pipe"
source: https://www.bctengineer.com/q/semester_6/hydro_power/water-hammer-cast-iron-pipe
site: BCT Engineering
---

# Water hammer in elastic cast-iron pipe

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

- Asked in: 2075 Bhadra, 1+2+5 marks
- Video: [What is Water Hammer?](https://www.youtube.com/watch?v=xoLmVFAFjn4) — Practical Engineering
- 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-cast-iron-pipe
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-1

## Question

What is water hammer? Write down the problems with water hammer. Water is flowing through a cast-iron pipe of diameter 150 mm and thickness 10 mm which is provided with a valve at its end. Water is suddenly stopped with closing the valve. Find the maximum velocity of water, when rise of pressure due to sudden closure of valve is 1.962 MN/m². Take K = 1.962 GN/m² and E = 117.7 GN/m².

## Short answer

Water hammer is sudden pressure rise when flow stops abruptly; causes pipe burst, cavitation, vibration. For elastic pipe, maximum velocity V = p/√(ρ/(1/K + D/Et)) = 1.57 m/s given p=1.962 MN/m².

## Answer

#### Water hammer
**Water hammer** is the sudden rise (and following fall) of pressure in a pipe when the flowing water is suddenly stopped or its velocity is suddenly changed, e.g. by quick closing of a valve or sudden load rejection at a turbine. The kinetic energy of the moving water is turned into pressure energy, and a pressure wave travels back and forth along the pipe at the speed of sound in water.

#### Problems caused by water hammer
- Very high pressure can burst the pipe or penstock.
- Negative pressure in the return wave can cause collapse of thin pipes and cavitation.
- Damage to valves, joints, anchors and supports; noise and vibration.
- Need for thicker (costlier) pipes and protective devices like surge tanks and relief valves.
- Unstable turbine governing.

#### Numerical: elastic pipe, sudden closure
Data: $D = 0.15$ m, $t = 0.01$ m, $p = 1.962$ MN/m², $K = 1.962$ GN/m², $E = 117.7$ GN/m², $\rho = 1000$ kg/m³.

For sudden closure in an **elastic** pipe:
$$
p = V\sqrt{\frac{\rho}{\dfrac{1}{K} + \dfrac{D}{E\,t}}}
$$

$$
\begin{aligned}
\frac{1}{K} + \frac{D}{Et} &= \frac{1}{1.962 \times 10^9} + \frac{0.15}{117.7 \times 10^9 \times 0.01} \\
&= 5.097 \times 10^{-10} + 1.274 \times 10^{-10} = 6.371 \times 10^{-10}\ \text{m}^2/\text{N} \\
\sqrt{\frac{1000}{6.371 \times 10^{-10}}} &= 1.2528 \times 10^6 \\
V &= \frac{1.962 \times 10^6}{1.2528 \times 10^6} = 1.566\ \text{m/s}
\end{aligned}
$$

**Answer:** Maximum velocity of water ≈ 1.57 m/s.

## Check yourself

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

1. What is water hammer?
   A. Steady pressure drop due to friction
   B. Sudden pressure rise and fall when flow is suddenly stopped or changed
   C. Air entering a pipe
   D. Slow oscillation of the free surface in a tank
   Answer: B. Sudden stopping converts kinetic energy to pressure energy and a pressure wave moves along the pipe. (Key point: Definition)

2. Which problem is caused by the negative-pressure phase of water hammer?
   A. Pipe collapse and cavitation
   B. Increased turbine efficiency
   C. Reduced noise
   D. Higher discharge
   Answer: A. Low pressure in the return wave can collapse thin pipes and cause cavitation. (Key point: Problems)

3. Which formula is used for sudden closure in an elastic pipe?
   A. p = V sqrt(K rho)
   B. p = V sqrt(rho / (1/K + D/(E t)))
   C. p = rho L V / T
   D. p = rho g H
   Answer: B. Pipe elasticity adds the D/(Et) term to the 1/K compressibility term. (Key point: Elastic pipe formula)

4. With the data given, what is the maximum velocity?
   A. 0.157 m/s
   B. 15.7 m/s
   C. 1.57 m/s
   D. 3.14 m/s
   Answer: C. 1/K + D/Et = 6.371 x 10^-10, sqrt(rho/that) = 1.2528 x 10^6, so V = 1.962 x 10^6 / 1.2528 x 10^6 = 1.566 m/s. (Key point: Result)

## 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 250 m penstock](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Awater-hammer-250m-penstock) — Hydro Power, chapter 1
- [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 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
- [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
- [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
- [Cast iron pipe with 85% magnesia insulation](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Acast-iron-pipe-magnesia-insulation-thickness) — Fundamental of Thermodynamics & Heat Transfer, chapter 7
- [Water hammer in 20 m steel pipeline with valve](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Awater-hammer-20m-pipeline-pressure-time-curves) — Hydraulics, chapter 4