---
title: "Water hammer in 200 mm pipe"
subject: "Hydro Power"
chapter: 1
key: "semester_6/hydro_power:water-hammer-200mm-pipe"
source: https://www.bctengineer.com/q/semester_6/hydro_power/water-hammer-200mm-pipe
site: BCT Engineering
---

# Water hammer in 200 mm pipe

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

- Asked in: 2081 Asoj, 2+2 marks
- Video: [Water Hammer - The Joukowsky Equation (3/8)](https://www.youtube.com/watch?v=GfCCsdHKrF8) — EngineeringTrainer
- 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-200mm-pipe
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-1

## Question

Water is flowing in a 200 mm diameter pipe with a velocity of 2 m/s. If the pipe is abruptly closed, calculate the pressure rise due to water hammer and the period of oscillation of the pressure wave. Assume the wave speed in the pipe is 1400 m/s.

## Short answer

Pressure rise Δp = ρcV = 2.8 MPa (285.4 m head). Period T = 4L/c = L/350 s (e.g., 2.86 s for L=1000 m). Diameter does not affect pressure rise for abrupt closure.

## Answer

For abrupt (instantaneous) closure, the pressure rise is given by Joukowsky's equation and does not depend on the pipe diameter.

#### Pressure rise
$$
\begin{aligned}
\Delta p &= \rho c V = 1000 \times 1400 \times 2 = 2.8 \times 10^6\ \text{N/m}^2 = 2.8\ \text{MPa} \\
\Delta H &= \frac{cV}{g} = \frac{1400 \times 2}{9.81} = 285.4\ \text{m of water}
\end{aligned}
$$

#### Period of oscillation
One full cycle of the pressure wave takes four trips along the pipe:
$$
T = \frac{4L}{c} = \frac{4L}{1400} = \frac{L}{350}\ \text{s}
$$
The pipe length L is not given, so T is left in terms of L. For example, for $L = 1000$ m, $T = 4 \times 1000/1400 = 2.86$ s.

**Answer:** Pressure rise = 2.8 MN/m² (≈ 285.4 m head); period $T = 4L/c = L/350$ s (2.86 s if L = 1000 m).

## Check yourself

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

1. For abrupt closure, which formula gives the pressure rise?
   A. rho L V / T
   B. rho c V
   C. rho V^2 / 2
   D. V sqrt(g D)
   Answer: B. Joukowsky: delta p = rho c V, giving 2.8 MPa here. (Key point: Joukowsky equation)

2. How does the 200 mm diameter affect the pressure rise?
   A. Larger diameter gives larger rise
   B. Smaller diameter gives larger rise
   C. It does not affect it
   D. The rise is proportional to diameter squared
   Answer: C. The Joukowsky rise depends on c and V only, not on pipe diameter. (Key point: Effect of diameter)

3. Why can the period not be given as a number here?
   A. The wave speed is unknown
   B. The velocity is unknown
   C. The pipe length L is not given and T = 4L/c depends on it
   D. Period depends on the diameter only
   Answer: C. T = 4L/c = L/350 s, so it needs L. (Key point: Period)

4. What is the pressure rise expressed as head of water?
   A. 285.4 m (cV/g)
   B. 28.5 m
   C. 2800 m
   D. 14.3 m
   Answer: A. delta H = cV/g = 1400 x 2/9.81 = 285.4 m. (Key point: Head form)

## 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
- [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
- [Pipe flow regimes and velocity profiles](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Apipe-flow-regimes-profiles) — 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

- [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×
- [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
- [Water hammer pressure and stress, 2300 m pipeline](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Awater-hammer-2300m-pressure-stress-1725m) — 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