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How to Calculate Pipe Size: Formula, Continuity Equation & Derivation

Reviewed by PipeSizingCalculator Engineering Team Updated October 31, 2026 Reading Time: 6 min

1. The Law of Conservation of Mass

In fluid mechanics, the continuity equation derives from the conservation of mass. For steady, one-dimensional, incompressible fluid flow (such as liquid water at ambient pressures), mass flow rate $\dot{m}$ remains constant across every cross-section:

$\dot{m} = ho \cdot Q = ho \cdot v \cdot A = ext{constant}$

Dividing by constant density $ ho$ yields the volumetric continuity equation: $Q = v \cdot A$.

2. Solving for Required Internal Bore

For a circular conduit of inside diameter $D$, the cross-sectional flow area is $A = rac{\pi D^2}{4}$. Substituting into the continuity equation:

$Q = v \cdot \left( rac{\pi D^2}{4} ight) \implies D^2 = rac{4Q}{\pi v} \implies D = \sqrt{ rac{4Q}{\pi v}}$

3. Step-by-Step Worked Example

Suppose a commercial branch line requires a simultaneous design flow rate of $Q = 0.75 ext{ L/s}$ ($0.00075 ext{ m}^3 ext{/s}$), with a target velocity of $v = 1.20 ext{ m/s}$:

Step 1: Convert units to SI: Q = 0.00075 m³/s, v = 1.20 m/s

Step 2: D_req = sqrt( (4 × 0.00075) / (π × 1.20) )

Step 3: D_req = sqrt( 0.0030 / 3.7699 ) = sqrt( 0.00079577 ) = 0.02821 m

Step 4: D_req = 28.21 mm

Looking up standard BS EN 1057 copper tube: 28mm tube has an internal diameter of 26.2 mm (too small, velocity would be 1.39 m/s). 35mm tube has an internal bore of 32.6 mm, yielding an actual velocity of 0.90 m/s. Therefore, a 35mm tube is selected for low-noise commercial installations.