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How It Works
The continuity equation Q = A × v expresses conservation of mass for incompressible flow: the volumetric flow rate stays constant along a pipe. When a pipe narrows the velocity must increase, and vice versa. This principle underlies Venturi meters, nozzles, and pipe-sizing calculations in plumbing and HVAC.
Example Problem
Water flows through a 100 mm diameter pipe at 3 m/s. What is the volumetric flow rate?
- Pipe area: A = π/4 × (0.1)² = 0.00785 m²
- Q = 0.00785 × 3 = 0.02356 m³/s (about 23.6 L/s)
Frequently Asked Questions
What is the continuity equation in fluid mechanics?
Q = A × v states that volumetric flow rate equals cross-sectional area multiplied by velocity. It assumes the fluid is incompressible and the flow is steady.
Why does velocity increase when a pipe narrows?
Because the same volume of fluid must pass through a smaller area per unit time. If the area halves, the velocity doubles. This is the Venturi effect.
What is a safe pipe flow velocity for water?
Typical design velocities are 1–3 m/s for water supply and up to 5 m/s for short runs. Velocities above 3 m/s increase erosion risk and noise in metal pipes.
Related Calculators
- Bernoulli Theorem Calculator — extends continuity with pressure and elevation terms.
- Venturi Meter Calculator — uses continuity to measure flow via a constriction.
- Pipe Flow Calculator — compute Reynolds number and flow rate for circular pipes.
- Density Calculator — find density, mass, or volume for compressible flow analysis.
- Volume Converter — convert between liters, gallons, cubic meters, and other volume units.