The pipe cross-section is halved at a constriction. How does velocity change? What happens to pressure?

You can work it out this way: apply continuity A₁v₁ = A₂v₂ first, then Bernoulli.

Using Bernoulli's principle, explain why an airplane wing generates lift.

You can work it out this way: consider the upper versus lower surface curvature and resulting flow speeds.

Inlet A₁ = 0.1 m² with v₁ = 2 m/s, outlet A₂ = 0.05 m². What is the outlet velocity and pressure change (ρ = 1000 kg/m³)?

You can work it out this way: use continuity for velocity, then ΔP = ½ρ(v₂² − v₁²).

Pro 🔒~25 min

Bernoulli's Principle & Fluid Flow

Discover why faster flow means lower pressure — from Venturi tubes to airplane wings

How it works

Bernoulli's equation is an energy conservation statement for steady, incompressible flow: the sum of static pressure, dynamic pressure (½ρv²), and hydrostatic pressure (ρgh) remains constant along a streamline. The continuity equation A₁v₁ = A₂v₂ forces fluid to accelerate through a constriction, which Bernoulli's equation then links to a corresponding pressure drop. Airfoil lift arises because the curved upper surface accelerates flow, lowering pressure above the wing.

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Step-by-step

Increase the inlet velocity and area ratio to see the pressure difference build in the Venturi section.
The color gradient along the pipe shows high (blue) to low (red) pressure regions.
Unlock Pro mode to change fluid density and add a height difference between inlet and outlet.

Key formulas

$P + \frac{1}{2}\rho v^2 + \rho g h = \text{const}$ Bernoulli's Equation
$A_1 v_1 = A_2 v_2$ Continuity Equation (incompressible flow)
$\Delta P = \frac{1}{2}\rho(v_2^2 - v_1^2)$ Pressure difference from velocity change

Frequently asked questions

The pipe cross-section is halved at a constriction. How does velocity change? What happens to pressure?: You can work it out this way: apply continuity A₁v₁ = A₂v₂ first, then Bernoulli.
Using Bernoulli's principle, explain why an airplane wing generates lift.: You can work it out this way: consider the upper versus lower surface curvature and resulting flow speeds.
Inlet A₁ = 0.1 m² with v₁ = 2 m/s, outlet A₂ = 0.05 m². What is the outlet velocity and pressure change (ρ = 1000 kg/m³)?: You can work it out this way: use continuity for velocity, then ΔP = ½ρ(v₂² − v₁²).