Fluid Flow Calculator — Flow Rate and Continuity Equation
Calculate fluid flow rate, velocity, and pipe dimensions using the continuity equation Q = Av. Covers Bernoulli's principle, Reynolds number, and pipe flow.
Fluids in pipes and channels follow predictable rules. Speed up the fluid and it has to go through a narrower section. Increase the pipe diameter and flow slows down. These relationships — captured in the continuity equation and Bernoulli's principle — explain everything from garden hose nozzles to aircraft wing lift to how your heart pumps blood.
The CalcHub fluid flow calculator computes flow rate, fluid velocity, and pipe cross-sections using fluid continuity.
The Continuity Equation
Q = A × vFor incompressible flow between two cross-sections:
A₁v₁ = A₂v₂
- Q = volumetric flow rate (m³/s)
- A = cross-sectional area (m²)
- v = fluid velocity (m/s)
Bernoulli's Principle
For an ideal fluid in steady flow:
P + ½ρv² + ρgh = constant
Where the fluid speeds up, pressure drops. This explains:
- Venturi meters (measure flow via pressure drop)
- Airplane lift (faster air over wing = lower pressure = upward force)
- The Coanda effect
- Why a shower curtain blows inward
Flow Rate Reference
| Application | Typical Flow Rate |
|---|---|
| Garden hose | 10–30 L/min |
| Kitchen tap | 6–12 L/min |
| Shower head | 8–15 L/min |
| Fire hydrant | 1500–2000 L/min |
| Human aorta | 5–6 L/min (cardiac output) |
Worked Example
Water flows through a pipe with 5 cm diameter at 2 m/s. It enters a narrower section with 2 cm diameter. Find the new velocity.
A₁ = π × (0.025)² = 1.963 × 10⁻³ m²
A₂ = π × (0.010)² = 3.14 × 10⁻⁴ m²
A₁v₁ = A₂v₂
1.963 × 10⁻³ × 2 = 3.14 × 10⁻⁴ × v₂
v₂ = 3.927 × 10⁻³ / 3.14 × 10⁻⁴ = 12.5 m/s
Area ratio = 6.25:1, velocity ratio = 6.25:1. That's the continuity equation at work.
What is the Reynolds number?
Re = ρvL/μ, where μ is dynamic viscosity and L is a characteristic length (pipe diameter). Low Re (< ~2000) = smooth laminar flow. High Re (> ~4000) = turbulent. Between them is transitional flow. Laminar flow in pipes follows precise analytical equations; turbulent flow requires empirical factors.
What's the difference between volumetric and mass flow rate?
Volumetric flow rate Q (m³/s) ignores density. Mass flow rate ṁ (kg/s) = ρQ. For gases, density changes with pressure and temperature, so mass flow rate is more useful. For liquids (nearly incompressible), volumetric flow rate is usually preferred.
How does pipe friction affect flow?
Real pipes have friction losses described by the Darcy-Weisbach equation: ΔP = f × (L/D) × (ρv²/2), where f is the friction factor. Longer pipes, smaller diameters, and higher velocities all increase pressure drop. This determines pump sizing for piping systems.