Skip to main content

Penstock thickness (1.3 m, 20 kg/cm²)

Short answer

Design pressure p = 1.20 × 20 = 24 kg/cm². Thickness t = pD/(2 σ η_j) = (24 × 130)/(2 × 1050 × 0.90) = 1.651 cm = 16.51 mm, so use 17 mm.

Calculate the thickness of a penstock pipe with an internal diameter of 1.3 m that conveys water under a pressure head of 20 kg/cm², considering a 20% potential increase in pressure due to water hammer. Use a design stress of 1050 kg/cm² and a joint efficiency of 90%.

Given: D=1.3D = 1.3 m =130= 130 cm, pressure p0=20p_0 = 20 kg/cm², water hammer rise 20%, design stress σ=1050\sigma = 1050 kg/cm², joint efficiency ηj=0.90\eta_j = 0.90.

Formula (hoop stress in a thin pipe):

t=p D2 σ ηjt = \frac{p\,D}{2\,\sigma\,\eta_j}

Design pressure

p=1.20×20=24 kg/cm2p = 1.20 \times 20 = 24\ \text{kg/cm}^2

Thickness

t=24×1302×1050×0.90=31201890=1.651 cm=16.51 mm\begin{aligned} t &= \frac{24 \times 130}{2 \times 1050 \times 0.90} \\ &= \frac{3120}{1890} = 1.651\ \text{cm} = 16.51\ \text{mm} \end{aligned}

Answer: penstock thickness t=16.5t = 16.5 mm, say 17 mm (plus about 2 mm corrosion allowance if required).

✓ Answer checked by Claude Opus 5.5 (high effort)

Related questions

All Hydro Power chapter 5 questions →