Pipe Flow Calculator
Calculate flow rate, velocity, pressure drop, and Reynolds number for pipes using Darcy-Weisbach.
📖 What is a Pipe Flow Calculator?
A pipe flow calculator determines how fluids move through pipes under pressure. It is used daily by plumbing engineers, civil engineers, HVAC designers, and process engineers to size pipes correctly, estimate pressure losses, and ensure systems deliver the required flow rate to where it is needed.
This calculator applies the Darcy-Weisbach equation - the most accurate and universal model for pipe friction losses. Unlike the older Hazen-Williams formula (which only applies to water), Darcy-Weisbach works for any Newtonian fluid at any temperature and any pipe material, in both laminar and turbulent regimes.
Two modes are available: Find Pressure Drop calculates how much pressure is lost for a given flow rate through a pipe - used when you know the required flow and need to know the pump head required. Find Flow Rate calculates how much flow a pipe delivers given the available pressure head - used when designing gravity-fed systems or checking existing pipework.
The calculator also computes the Reynolds number to classify the flow regime (laminar or turbulent), and the Darcy friction factor using the Swamee-Jain approximation (accurate within 3% for turbulent flows). For laminar flow (Re < 2300), it uses the exact formula f = 64/Re.
📝 Pipe Flow Formulas
Flow velocity:
v = Q / A where A = π(D/2)²
Reynolds number:
Re = v × D / ν
Friction factor (Swamee-Jain, turbulent Re > 4000):
f = 0.25 / [log₁₀(ε/(3.7D) + 5.74/Re⁰·⁹)]²
Laminar (Re ≤ 2300): f = 64/Re
Darcy-Weisbach pressure drop:
ΔP = f × (L/D) × (ρv²/2) [Pa]
Head loss: h_f = ΔP / (ρg) [m]
Where: Q = flow rate (m³/s) | D = diameter (m) | ν = kinematic viscosity (m²/s) | ε = roughness (m) | L = length (m) | ρ = density (kg/m³) | g = 9.81 m/s²
v = Q / A where A = π(D/2)²
Reynolds number:
Re = v × D / ν
Friction factor (Swamee-Jain, turbulent Re > 4000):
f = 0.25 / [log₁₀(ε/(3.7D) + 5.74/Re⁰·⁹)]²
Laminar (Re ≤ 2300): f = 64/Re
Darcy-Weisbach pressure drop:
ΔP = f × (L/D) × (ρv²/2) [Pa]
Head loss: h_f = ΔP / (ρg) [m]
Where: Q = flow rate (m³/s) | D = diameter (m) | ν = kinematic viscosity (m²/s) | ε = roughness (m) | L = length (m) | ρ = density (kg/m³) | g = 9.81 m/s²
✍️ How to Use This Calculator
- Select Find Pressure Drop (you know flow) or Find Flow Rate (you know available head).
- Enter the pipe inner diameter in mm and length in metres.
- Enter the flow rate in L/s (or available pressure head in metres).
- Enter the pipe roughness ε in mm. Common values: PVC = 0.0015, copper = 0.0015, galvanised steel = 0.15, cast iron = 0.26.
- Select the fluid - water at 20°C is the default.
- Click Calculate. Review velocity (aim for 0.5–3 m/s), Reynolds number (flow regime), and pressure drop.
📄 Example Calculations
Example 1 - Water supply riser pipe:
Pipe: 50 mm dia PVC, 100 m long, ε = 0.0015 mm, water at 20°C, flow = 2 L/s
Area = π × (0.025)² = 0.001963 m²
v = 0.002 / 0.001963 = 1.02 m/s ✓ (within 0.5–3 m/s)
Re = 1.02 × 0.05 / 1.004×10⁻⁶ = 50,797 (turbulent)
f (Swamee-Jain) ≈ 0.0198
ΔP = 0.0198 × (100/0.05) × (998 × 1.02²/2) = 20.6 kPa = 2.1 m head
Example 2 - Larger diameter comparison:
Same conditions but 80 mm pipe: v = 0.398 m/s, ΔP = 1.5 kPa = 0.15 m head
Doubling diameter reduces pressure drop by ~14× - pipe diameter has an enormous impact on flow resistance. Try this example →
Pipe: 50 mm dia PVC, 100 m long, ε = 0.0015 mm, water at 20°C, flow = 2 L/s
Area = π × (0.025)² = 0.001963 m²
v = 0.002 / 0.001963 = 1.02 m/s ✓ (within 0.5–3 m/s)
Re = 1.02 × 0.05 / 1.004×10⁻⁶ = 50,797 (turbulent)
f (Swamee-Jain) ≈ 0.0198
ΔP = 0.0198 × (100/0.05) × (998 × 1.02²/2) = 20.6 kPa = 2.1 m head
Example 2 - Larger diameter comparison:
Same conditions but 80 mm pipe: v = 0.398 m/s, ΔP = 1.5 kPa = 0.15 m head
Doubling diameter reduces pressure drop by ~14× - pipe diameter has an enormous impact on flow resistance. Try this example →
Frequently Asked Questions
What is the Darcy-Weisbach equation?
The Darcy-Weisbach equation calculates pressure loss due to friction in a pipe: ΔP = f × (L/D) × (ρv²/2), where f is the Darcy friction factor, L is pipe length, D is diameter, ρ is fluid density, and v is average flow velocity. It is the most accurate and widely applicable equation for pipe flow, valid for any fluid, any pipe material, and both laminar and turbulent flow.
What is the Reynolds number?
The Reynolds number (Re) is a dimensionless number that characterises flow regime: Re = ρvD/μ = vD/ν, where v is velocity, D is diameter, and ν is kinematic viscosity. Re < 2300 is laminar flow (smooth, layered). Re > 4000 is turbulent (chaotic mixing). Between 2300–4000 is a transitional zone. Most engineering pipe flows are turbulent.
How do I find the friction factor?
For laminar flow: f = 64/Re. For turbulent flow, use the Colebrook-White equation (implicit) or the explicit Swamee-Jain approximation: f = 0.25 / [log₁₀(ε/(3.7D) + 5.74/Re⁰·⁹)]². This calculator uses the Swamee-Jain formula for turbulent flow - accurate to within 3% for Re from 10⁴ to 10⁸.
What units does this calculator use?
This calculator uses SI units throughout: diameter in millimetres (mm), length in metres (m), flow rate in litres per second (L/s), velocity in m/s, pressure drop in kilopascals (kPa), and roughness in millimetres (mm). Water at 20°C is the default fluid (density 998 kg/m³, kinematic viscosity 1.004 × 10⁻⁶ m²/s).
What is pipe roughness and how does it affect flow?
Pipe roughness (ε) is the average height of surface irregularities on the pipe inner wall, measured in mm. Higher roughness creates more turbulence near the wall, increasing the friction factor and pressure drop. Smooth pipes (PVC, drawn copper) have ε ≈ 0.0015 mm; old cast iron pipes can have ε > 0.5 mm from corrosion and scale. Roughness only matters in turbulent flow - in laminar flow, pressure drop is independent of roughness.
What is the Reynolds number and why does it matter?
The Reynolds number (Re) is a dimensionless parameter that predicts the flow regime in a pipe. Re = (density x velocity x diameter) / dynamic viscosity. Re < 2,300: laminar flow (smooth, parallel layers). Re > 4,000: turbulent flow (chaotic, mixing layers). 2,300-4,000: transitional flow. Turbulent flow has higher friction losses and requires more pumping energy. Most water supply systems operate in turbulent flow. Knowing Re helps select the correct friction factor for pressure drop calculations.
What pipe diameter should I use for a given flow rate?
A practical guideline for water supply systems: flow velocity should be 0.5-3 m/s for supply pipes (2 m/s is a common design target). Higher velocities increase pressure drop and noise. For a 2 m/s target velocity: pipe cross-sectional area needed = flow rate / velocity. Example: 10 L/s (0.01 m^3/s) at 2 m/s: area = 0.01/2 = 0.005 m^2. Diameter = sqrt(4 x 0.005 / pi) = 0.080 m = 80 mm pipe. Round up to the nearest standard pipe size.
What is the Darcy-Weisbach equation and when do I use it?
The Darcy-Weisbach equation calculates pressure loss due to friction in a pipe: delta-P = f x (L/D) x (rho x V^2 / 2), where f is the Darcy friction factor, L is pipe length, D is diameter, rho is fluid density, and V is flow velocity. It is the most accurate method for pressure drop calculation and applies to all flow regimes (laminar and turbulent) and all pipe materials. Use it for water supply, HVAC, oil pipelines, and process engineering. The friction factor f is determined from the Moody chart or the Colebrook-White equation using the Reynolds number and pipe roughness.
What is a typical friction factor for commercial steel pipe?
For commercial steel pipe (roughness 0.046 mm) in the turbulent fully rough regime, friction factor f is approximately 0.01-0.02 depending on Reynolds number and relative roughness. This calculator uses the Swamee-Jain approximation, accurate within 3% of the Colebrook-White equation for most practical flow conditions.