Tools › Fluids and Heat Transfer › Pipe Flow › Pipe Flow › Example

Moody's chart illustration: head loss and pressure drop in 200 ft of 6-in asphalted cast-iron pipe at 6 ft/s (White Example 6.7)

ToolPipe Flow
SourceMoody, L. F. (1944). "Friction Factors for Pipe Flow." Transactions of the ASME, Vol. 66, No. 8, pp. 671–684 (Example 1 of the illustration of use of charts, p. 673); White, F. M. (2011). Fluid Mechanics, 7th ed. McGraw-Hill, New York. Example 6.7.
LevelUndergraduate

Problem

Water at 60 °F flows at a mean velocity of 6 ft/s through 200 ft of horizontal 6-in-diameter asphalted cast-iron pipe. Find the Reynolds number, the Darcy friction factor, the head loss and the pressure drop.

Inputs to Enter

  • Fluid water at 60 °F (NIST table: ρ = 62.36 lb/ft³, μ = 1.121 cP, ν = 1.208e-5 ft²/s; Moody used ν = 1.216e-5, White 1.1e-5)
  • Custom inside diameter 6 in, length 200 ft, asphalted cast iron (ε = 0.0004 ft, ε/D = 0.0008), solve for the head loss from the velocity 6 ft/s, no fittings, no elevation change
Open the Pipe Flow tool (loaded with this example)

Answers

  • Q = V A = 528.8 gpm; Re = ρ V D/μ = 248,300 (Moody 2.5 × 10⁵, White 273,000 with his ν)
  • Colebrook f = 0.01994 (Swamee–Jain 0.02008, Haaland 0.01982); Moody read f ≈ 0.02 from the chart
  • h_f = f (L/D) V²/(2g) = 0.01994 (200/0.5)(6²/64.35) = 4.462 ft (Moody and White: 4.5 ft)
  • Δp = ρ g h_f = 1.932 psi = 278 lbf/ft² (White: about 280 lbf/ft²); hydraulic power 0.596 hp

Notes

The tool's default inputs are this case; press Submit. The printed values are chart readings, which the Colebrook solution reproduces within 1 %. The tool's other problems reproduce White's Example 6.9 (flow from a head loss: Re 72,600, V 4.84 m/s, Q 0.342 m³/s), Example 6.11 (diameter 0.30 m) and Example 6.16 (ΣK 12.2, about 86 hp) as checked in test_pipe_flow.php.