Area Ratio Calculator

Compute β = A₁/A₂ for pipe contractions, expansions, Venturi meters, and nozzles — and derive the velocity ratio from continuity.

Fluid Mechanics I

Inputs

For each section enter either the diameter or the cross-sectional area.

Section 1 (upstream)

Diameter D (mm)

Cross-sectional area A (m²)

Computed from diameter

Section 2 (downstream)

Diameter D (mm)

Cross-sectional area A (m²)

Computed from diameter

Velocity at section 1 (optional) V₁ (m/s)

If provided, V₂ = V₁ × β is calculated.

Theory

Area ratio:

β = A₁ / A₂ = (D₁/D₂)²

Velocity ratio from continuity:

V₂ / V₁ = A₁ / A₂ = β

Common applications:

Venturi meter — β = (D₂/D₁)² is the throat-to-pipe area ratio
Pipe contraction / expansion — velocity changes by factor β
Nozzle design — area ratio controls Mach number in compressible flow
Minor loss coefficients — many depend on the area ratio

For incompressible flow, the continuity equation A₁V₁ = A₂V₂ means velocity is inversely proportional to area. A smaller section 2 (β > 1) accelerates the flow; a larger section 2 (β < 1) decelerates it. The Venturi meter exploits this velocity change to infer flow rate from a pressure difference.