Fluid Velocity Calculator
Velocity (m/s)
10
How it works
Fluid velocity in a pipe or channel can be calculated from volumetric flow rate and cross-sectional area: v = Q / A, where Q is flow rate (m³/s) and A is the cross-sectional area (m²).
**Continuity equation** For incompressible flow, mass is conserved: A₁v₁ = A₂v₂ (continuity equation). When a pipe narrows, velocity increases proportionally. A pipe narrowing from 100 mm diameter to 50 mm diameter doubles the velocity. This relationship is fundamental to venturi meters, nozzle design, and flow control.
**Velocity profile in pipe flow** In laminar pipe flow, velocity has a parabolic profile — zero at the wall (no-slip condition), maximum at centerline (v_max = 2 × v_average). In turbulent flow, the profile is much flatter but still zero at the wall. Flow meters often measure velocity at a specific point — the conversion factor to average velocity depends on flow regime.
**Critical velocity and erosion** At high flow velocities, erosion of pipe walls and fittings occurs. Maximum recommended velocities: water in steel pipe 3–5 m/s, slurry 2–3 m/s, steam 20–40 m/s, natural gas 15–20 m/s. Exceeding these values accelerates corrosion and erosion, especially at elbows and fittings where flow direction changes.
**Choked flow** In compressible gas flow, when the pressure ratio exceeds a critical value (≈2:1 for air), the flow at the restriction reaches the speed of sound (Mach 1) — further pressure reduction cannot increase mass flow. This is choked flow, important in safety relief valve sizing and compressed gas system design.
Frequently Asked Questions
- Recommended velocities: cold water supply branches 1.5–3 m/s, mains 0.5–1.5 m/s. Hot water: slightly lower to reduce erosion at high temperatures. Above 3 m/s in copper pipe: erosion and noise become problems. Above 1.5 m/s in galvanized steel: corrosion accelerates. For HVAC chilled water: 1–3 m/s. Domestic sewer pipes (gravity): must maintain self-cleaning velocity of at least 0.6 m/s at design flow to prevent sediment deposition — this minimum velocity requirement governs pipe size and slope in drainage design.
- Pitot tube: measures stagnation - static pressure difference → v = √(2ΔP/ρ). Must be at known pipe cross-section for flow rate. Ultrasonic: transit-time measurement between transducers (non-invasive, clamp-on). Electromagnetic (magmeters): for conductive liquids (water, slurry) — no moving parts, low maintenance, ±0.5% accuracy. Rotameters (variable area meters): glass tube with float, simple, cheap, low accuracy. Vortex meters: count vortex shedding frequency from bluff body. Thermal mass flow: measures heat transfer to/from a heated element proportional to mass flow rate — accurate for gas flows.
- Too low velocity: sediment deposition in sewers (below 0.6 m/s), biological growth in water mains, poor heat transfer in process pipes, and poor mixing. Too high velocity: erosion of pipe walls and fittings (above 3–5 m/s for water), noise and vibration, water hammer on sudden valve closure (pressure spike = ρ × v × c_sound), and excessive pressure drop requiring larger pumps. Pipe sizing balances these constraints: size to achieve target velocity at design flow rate, verify pressure drop is within available head, and check for minimum velocity at reduced flow conditions.
- Laminar flow: parabolic profile — v(r) = v_max × (1 - (r/R)²), v_max = 2 × v_average. Center velocity is double the average. Turbulent flow: much flatter profile — approximately v(r) = v_max × (1 - r/R)^(1/n) where n ≈ 7 for Re ≈ 100,000. The 'turbulent 1/7 power law' gives v_max ≈ 1.2 × v_average. Flow meters positioned at the pipe centerline over-read by 2× in laminar flow but only ~20% in turbulent flow — this is why flow meters specify a minimum straight pipe run (10–20 pipe diameters) to ensure fully developed turbulent profile.