Fluid Flow Through Pipes
The continuity equation links flow rate, velocity, and cross-sectional area. Use it to size pipes and predict pressure drops in hydraulic and HVAC systems.
Core Equations
Flow rate: Q = A × v (m³/s)
Velocity: v = Q / A (m/s)
Area: A = π × d² / 4 (m²)
Reynolds: Re = ρvd / μ
ρ = fluid density (kg/m³)
μ = dynamic viscosity (Pa·s)
Re < 2300: laminar | Re > 4000: turbulentWorked Example
100mm dia pipe, Q = 0.02 m³/s (water):
A = π × 0.1² / 4 = 0.00785 m²
v = 0.02 / 0.00785 = 2.55 m/s
Re = 1000 × 2.55 × 0.1 / 0.001 = 255,000
→ Turbulent flow (Re >> 4000)Common Flow Rates
- Domestic tap: 0.1–0.2 L/s (6–12 L/min)
- Shower head: 0.15 L/s (9 L/min typical)
- Building main supply: 1–5 L/s
- Industrial pump: 10–1000 L/s
Calculate pipe flow: Free Fluid Flow Calculator
Key Flow Equations
- Continuity equation: A₁V₁ = A₂V₂ (conservation of mass for incompressible flow)
- Bernoulli's equation: P + ½ρV² + ρgh = constant
- Flow rate: Q = A × V (m³/s = m² × m/s)
- Reynolds number: Re = ρVD/μ (laminar <2300, turbulent >4000)
- Darcy-Weisbach (pipe friction loss): ΔP = f(L/D)(ρV²/2)
Engineering Applications
Fluid flow calculations are central to HVAC design (duct sizing, fan selection), water supply systems (pipe sizing, pump head requirements), fire suppression systems (sprinkler flow rates), and industrial process piping. In HVAC, maximum duct velocity is limited to ~8 m/s for main ducts to control noise. Water supply mains are sized to maintain minimum pressure at peak demand. Sewerage is designed as open-channel flow (gravity), requiring minimum velocity ~0.7 m/s to prevent sediment deposition. Oil and gas pipelines run at much higher pressures (up to 100 bar) requiring careful analysis of friction losses over hundreds of kilometres.
Frequently Asked Questions
What is head pressure and how is it related to fluid flow?
Head (H, in metres) is the equivalent height of a fluid column that would produce a given pressure: P = ρgH. Pump head describes how high a pump can raise fluid against gravity (and friction). A pump rated at 30 m head can raise water 30 m vertically (ignoring friction). When friction losses in pipework are accounted for, the available head for elevation is reduced accordingly.
What is cavitation and why is it damaging?
Cavitation occurs when local fluid pressure drops below the vapour pressure, forming vapour bubbles. When these bubbles collapse near solid surfaces, the implosion generates intense local pressures that erode metal — pump impellers, valves, and propellers are commonly damaged. Cavitation is prevented by ensuring NPSH_available > NPSH_required for pumps, and by avoiding sharp bends and restrictions that create low-pressure zones.
What is viscosity and how does it affect flow?
Dynamic viscosity (μ, Pa·s) measures a fluid's resistance to shear — its "thickness." Water at 20°C: 1.0 mPa·s. Engine oil at 40°C: ~100 mPa·s. Honey: ~10,000 mPa·s. High-viscosity fluids require larger pipe diameters or higher pressures to achieve the same flow rate. Kinematic viscosity ν = μ/ρ (m²/s) is used in the Reynolds number and is tabulated in fluid property references.