Skip to main content

Design pipes AB and BC, 20,000 population, f = 0.04

Short answer

Use Darcy-Weisbach equation with f=0.04. For AB, calculated 299 mm, adopt 300 mm, velocity 1.47 m/s. For BC, calculated 245 mm, adopt 250 mm, velocity 2.12 m/s.

A part of water distribution system is shown in figure below. The average water requirement is 150 lpcd and water is distributed only from the service reservoir located at A for the population of 20,000 at the point C. Design pipes AB and BC. The minimum pressure to be maintained is 15 m and Darcy's coefficient of friction f is 0.04. Assume peak factor of 3. Calculate the velocity of water in pipes AB and BC.

[Figure: A (RL 200 m) to B (RL 170 m), length 1000 m; B to C (RL 150 m), length 500 m.]

Given data and flow

  • Population at C = 20,000, 150 lpcd, peak factor 3
  • Q=20000×150×3/86400=104.17Q = 20000 \times 150 \times 3/86400 = 104.17 lps =0.1042= 0.1042 m³/s (the full flow passes through both AB and BC)
  • RL: A = 200 m (HGL = 200 m), B = 170 m, C = 150 m; LAB=1000L_{AB} = 1000 m, LBC=500L_{BC} = 500 m
  • Minimum pressure 15 m (at B and C), Darcy friction factor f=0.04f = 0.04

Formula

hf=8fLQ2π2gD5⇒D=(8fLQ2π2g hf)1/5h_f = \frac{8 f L Q^2}{\pi^2 g D^5} \quad\Rightarrow\quad D = \left(\frac{8 f L Q^2}{\pi^2 g\, h_f}\right)^{1/5}

Pipe AB

  • Available head =200−170−15=15= 200 - 170 - 15 = 15 m
  • D=(8×0.04×1000×0.10422π2×9.81×15)1/5=299D = \left(\dfrac{8 \times 0.04 \times 1000 \times 0.1042^2}{\pi^2 \times 9.81 \times 15}\right)^{1/5} = 299 mm; adopt 300 mm
  • Actual hf=14.76h_f = 14.76 m; HGL at B =200−14.76=185.24= 200 - 14.76 = 185.24 m; residual head at B =15.24= 15.24 m (> 15 m, OK)
  • Velocity v=0.1042/(π×0.32/4)=1.47v = 0.1042/(\pi \times 0.3^2/4) = 1.47 m/s

Pipe BC

  • Available head =185.24−150−15=20.24= 185.24 - 150 - 15 = 20.24 m
  • D=245D = 245 mm; adopt 250 mm
  • Actual hf=18.36h_f = 18.36 m; HGL at C =166.88= 166.88 m; residual head at C =16.88= 16.88 m (> 15 m, OK)
  • Velocity v=0.1042/(π×0.252/4)=2.12v = 0.1042/(\pi \times 0.25^2/4) = 2.12 m/s

Answer: AB = 300 mm with v = 1.47 m/s; BC = 250 mm with v = 2.12 m/s. Both velocities are below 3 m/s, and the pressure at B and C stays above 15 m.

✓ Answer checked by Claude Opus 5.5 (high effort)

Related questions

All Water Supply Engineering chapter 7 questions →