---
title: "Water hammer effects and gradual closure"
subject: "Hydro Power"
chapter: 1
key: "semester_6/hydro_power:water-hammer-gradual-closure"
source: https://www.bctengineer.com/q/semester_6/hydro_power/water-hammer-gradual-closure
site: BCT Engineering
---

# Water hammer effects and gradual closure

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

- Asked in: 2071 Magh, 3+4 marks
- Video: [Derivations For Gradually Closure Of Valve In Water Hammer - Pipe Network and Water Hammer Effect](https://www.youtube.com/watch?v=vo4h87WH8MU) — Ekeeda
- 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-gradual-closure
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-1

## Question

What is water hammer and what are its effects? How the water hammer pressure is calculated for the gradual closure of the valve in the pipe?

## Short answer

Water hammer is pressure surge from sudden velocity reduction; effects include pipe burst, cavitation, vibration. For gradual closure (T > 2L/c), pressure rise p = ρLV/T derived from Newton's second law on water column.

## Answer

#### Water hammer and its effects
**Water hammer** is the sharp rise of pressure in a closed conduit when the velocity of the flowing liquid is suddenly reduced, for example by closing a valve at the end of a penstock. The moving water column is brought to rest, its kinetic energy changes to pressure energy, and a pressure wave travels up and down the pipe with wave speed $c$ until friction damps it.

Effects:
- Very high pressure; pipe may burst or joints may fail.
- Low (negative) pressure phase may collapse the pipe or cause cavitation.
- Hammering noise, vibration, damage to valves, anchors and turbine parts.
- Penstock must be made thicker; surge tanks or relief valves are needed.

#### Pressure for gradual closure
Closure is **gradual** when the closing time $T > \dfrac{2L}{c}$ (the reflected wave returns before closure ends).

Consider a pipe of length $L$, area $A$, initial velocity $V$, valve closed uniformly in time $T$.

```text
 Reservoir                         Valve
 ~~~~~|=============================|X
      |<------------ L ------------>|
          water mass = rho A L
```

1. Mass of water in pipe $= \rho A L$.
2. Uniform retardation $= \dfrac{V - 0}{T} = \dfrac{V}{T}$.
3. Retarding force by Newton's second law:
$$
F = \rho A L \cdot \frac{V}{T}
$$
4. This force is provided by the pressure rise $p$ acting on area $A$: $F = pA$.
5. Equating:
$$
\begin{aligned}
pA &= \frac{\rho A L V}{T} \\
p &= \frac{\rho L V}{T}, \qquad H = \frac{p}{\rho g} = \frac{LV}{gT}
\end{aligned}
$$

**Example:** $L = 2500$ m, $V = 1.5$ m/s, $T = 25$ s: $p = 1000 \times 2500 \times 1.5/25 = 150$ kN/m².

If $T < 2L/c$, the closure is **sudden** and $p = \rho c V$ (rigid pipe, $c = \sqrt{K/\rho}$).

## Check yourself

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

1. When is closure considered gradual?
   A. T < 2L/c
   B. T > 2L/c
   C. T = L/V
   D. T > L/g
   Answer: B. If the closing time exceeds 2L/c, the reflected wave returns before closure ends. (Key point: Gradual closure condition)

2. Which principle is used to derive the pressure for gradual closure?
   A. Bernoulli's equation
   B. Continuity only
   C. Newton's second law applied to the water column
   D. Manning's equation
   Answer: C. Force = mass x retardation = rho A L x V/T, supplied by the pressure rise acting on area A. (Key point: Derivation basis)

3. What is the resulting pressure rise?
   A. p = rho c V
   B. p = rho L V / T
   C. p = rho V / (L T)
   D. p = rho g L
   Answer: B. Equating pA = rho A L V/T gives p = rho L V / T, so H = LV/(gT). (Key point: Result)

4. Which is an effect of water hammer?
   A. Pipe may burst and valves may be damaged
   B. Pipe becomes smoother
   C. Friction loss disappears
   D. Discharge increases permanently
   Answer: A. High pressure can burst pipes or fail joints, and vibration damages valves and turbine parts. (Key point: Effects)

## Related in Hydro Power

- [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
- [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 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
- [Measuring pressure difference in a pipe](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Ameasuring-pressure-difference) — Hydro Power, chapter 1

## Related in other subjects

- [Rapid closure time and peak hammer pressure](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Acast-iron-pipe-rapid-closure-time-and-length) — Hydraulics, chapter 4
- [Hammer pressure for 4 s and 60 s closure](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Asteel-pipeline-61cm-hammer-4s-60s) — 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
- [Gradual valve closure with retardation law](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Agradual-valve-closure-head-at-valve) — Hydraulics, chapter 4