Pressure Drop in a Pipe
Inputs
Internal pipe diameter
D:=100mm=3.94 in
Pipe length
L:=50m=164.04 ft
Q:=0.01m^3/s=0.35 ft^3/s
Volumetric flow rate
rho:=1000kg/m^3=62.43 lb/ft^3
Fluid density (water)
Dynamic viscosity (water at 20°C)
mu:=0.001Pa·s=1e-03 kg/m/s
Pipe roughness (commercial steel)
eps:=0.046mm=1.81e-03 in
Calculations
A_pipe:=(pi)/(4)·D^2=0.08 ft^2
Pipe cross-sectional area
V:=(Q)/(A_pipe)=4.18 ft/s
Mean flow velocity
Re:=(rho·V·D)/(mu)=127323.95
Reynolds number (dimensionless)
rr:=(eps)/(D)=4.6e-04
Relative roughness
Friction Factor — Colebrook-White (explicit Swamee-Jain)
Valid for Re > 4000 and 10⁻⁶ ≤ ε/D ≤ 10⁻².
- Swamee-Jain approximation: f ≈ 0.25 / [log₁₀(ε/3.7D + 5.74/Re⁰·⁹)]²
f:=(0.25)/((log10((rr)/(3.7)+(5.74)/(Re^0.9)))^2)=0.02
Darcy friction factor (Swamee-Jain)
Pressure Drop
dP:=f·(L)/(D)·(rho·V^2)/(2)=1.15 psi
Pressure drop — Darcy-Weisbach
dP_kPa:=(dP)/(1000)=1.15e-03 psi
Pressure drop in kPa
h_L:=(dP)/(rho·9.81m/s^2)=2.66 ft
Head loss equivalent (m of fluid)
Results
- Reynolds number confirms flow regime (turbulent if Re > 4000).
- Friction factor computed via Swamee-Jain explicit approximation.
- Pressure drop and equivalent head loss shown below.
Reynolds number
Re=127323.95
Darcy-Weisbach friction factor
f=0.02
Total pressure drop
dP_kPa=1.15e-03 psi
Equivalent head loss
h_L=2.66 ft
Pipe Pressure Drop Calculation
Darcy-Weisbach method for pressure drop in a circular pipe with Moody friction factor.
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