--- title: "Water hammer in 1.2 m steel pipe, wall thickness" subject: "Hydraulics" chapter: 4 key: "semester_4/hydraulics:water-hammer-steel-pipe-thickness-1200mm" source: https://www.bctengineer.com/q/semester_4/hydraulics/water-hammer-steel-pipe-thickness-1200mm site: BCT Engineering --- # Water hammer in 1.2 m steel pipe, wall thickness Hydraulics · Chapter 4: Unsteady flow in pipes - Asked in: 2077 Chaitra, 4+4 marks - Video: [CE REVIEW - WEEK 1.2 | WATER HAMMER PRESSURE](https://www.youtube.com/watch?v=wIpWQSmYPnI) — Engr. Jobert S. De La Cruz - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/hydraulics/water-hammer-steel-pipe-thickness-1200mm - Whole chapter: https://www.bctengineer.com/md/semester_4/hydraulics/chapter-4 ## Question A steel pipe 1.20 m in diameter conveys 1.40 m³/s of water under a head of 300 m. A valve at the downstream end can be expected to close suddenly. Estimate the water hammer pressure due to this closure. Also determine the minimum thickness of the wall to the nearest millimetre needed to withstand the pressures involved. For steel: E = 210 kN/mm², and safe working stress = 0.1 kN/mm². For water: K = 2.10 kN/mm². ## Short answer By iterative solution of wave speed and thickness, c ≈ 1205 m/s, Δp ≈ 1.49 MPa. Minimum wall thickness to withstand static plus hammer pressure at safe stress 100 MPa is 27 mm. ## Answer **Data.** $D = 1.20$ m, $Q = 1.40$ m³/s, static head 300 m ($p_0 = \rho gH = 2.943$ MPa), $E = 210$ kN/mm² $= 210\times10^9$ Pa, safe stress $\sigma_s = 0.1$ kN/mm² $= 100$ MPa, $K = 2.10$ kN/mm² $= 2.1\times10^9$ Pa. Sudden closure, so the full Joukowsky rise applies. $$ V_0 = \frac{Q}{\pi D^2/4} = \frac{1.4}{1.1310} = 1.238\ \text{m/s} $$ #### Water hammer pressure The wave speed depends on the wall thickness $t$ (unknown): $$ c = \frac{\sqrt{K/\rho}}{\sqrt{1 + \dfrac{KD}{Et}}}, \qquad \Delta p = \rho cV_0 $$ *First estimate (rigid pipe, $t \to \infty$):* $c = \sqrt{K/\rho} = 1449$ m/s, so $\Delta p \approx 1.79$ MPa. This is the upper limit. #### Thickness The pipe must carry the maximum pressure $p_0 + \Delta p$ at the safe hoop stress: $$ \sigma_s = \frac{(p_0 + \Delta p)D}{2t} \;\Rightarrow\; t = \frac{(p_0 + \Delta p)D}{2\sigma_s} $$ Since $\Delta p$ depends on $t$, iterate. Start with $t$ = 10 mm and repeat: each new $t$ gives a new $c$ and $\Delta p$. The substitution converges to $$ t = 26.6\ \text{mm},\qquad c = 1202.9\ \text{m/s},\qquad \Delta p = \rho cV_0 = 1.489\ \text{MPa} $$ $$ p_0 + \Delta p = 2.943 + 1.489 = 4.432\ \text{MPa}, \qquad t = \frac{4.432\times10^6(1.2)}{2(100\times10^6)} = 26.6\ \text{mm} $$ To the nearest (larger) millimetre: **$t = 27$ mm**. Check with $t = 27$ mm: $c = 1205.8$ m/s, $\Delta p = 1.493$ MPa ($152.1$ m of water), maximum stress $= \dfrac{(2.943 + 1.493)\times10^6(1.2)}{2(0.027)} = 98.6$ MPa $\le 100$ MPa. **Answer:** Water hammer pressure rise $\approx 1.49$ MPa ($\approx 152$ m of water; $1.79$ MPa if the pipe were rigid); minimum wall thickness $\approx 27$ mm. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why must the thickness be found by iteration? A. The wave speed c, and so the pressure rise, depends on the wall thickness t B. The static head changes with time C. The flow rate depends on t only D. Water bulk modulus depends on t Answer: A. c includes the term KD/(Et), so delta p changes with t, which in turn sets the required t. (Key point: Wave speed depends on thickness) 2. What pressure is the wall designed for? A. Water hammer rise only B. Static pressure plus water hammer rise, p0 + delta p C. Static pressure only D. Static minus water hammer rise Answer: B. The pipe must carry the maximum pressure, 2.943 + 1.49 = about 4.43 MPa. (Key point: Design pressure) 3. Which relation and result give the thickness? A. t = (p0 + delta p) D / (2 sigma_s), about 27 mm B. t = p D / sigma_s, about 53 mm C. t = (p0 + delta p) D / (4 sigma_s), about 13 mm D. t = delta p D / (2 sigma_s), about 9 mm Answer: A. Thin-wall hoop stress gives sigma = pD/2t; with 4.43 MPa, D = 1.2 m and 100 MPa, t = 26.6 mm, rounded to 27 mm. 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