Interactive venturi-style constriction: adjust pipe diameters, inlet velocity, and inlet pressure to see continuity (A₁V₁=A₂V₂) and Bernoulli's equation (P₁+½ρV₁²+ρgh₁ = P₂+½ρV₂²+ρgh₂) play out live.
This simulator visualizes the venturi effect — the trade-off between velocity and pressure that occurs when an incompressible fluid flows through a pipe constriction. It applies the continuity equation and Bernoulli's equation together to compute the velocity and pressure at the throat from conditions at the inlet, and animates particles moving through the constriction so you can see flow speed up as the pipe narrows.
The continuity equation states that mass flow rate is conserved for an incompressible fluid in steady flow: A₁V₁ = A₂V₂, where A is the cross-sectional area and V is the average velocity at each point. Because area scales with the square of diameter, a constriction that reduces diameter by half quadruples the velocity: V₂ = V₁·(D₁/D₂)².
Bernoulli's equation is a statement of conservation of mechanical energy along a streamline for an inviscid, incompressible, steady flow: P₁ + ½ρV₁² + ρgh₁ = P₂ + ½ρV₂² + ρgh₂. As velocity increases through the throat, the ½ρV² (dynamic pressure) term grows, so the static pressure P must fall to keep the sum constant. This is why pressure at the throat of a venturi is lower than at the inlet — the basis for venturi flow meters, carburetors, and aspirators.
Set the inlet and throat diameters (D₁, D₂), the inlet velocity V₁, and the inlet gauge pressure P₁. The simulator computes the throat velocity from continuity, then solves Bernoulli's equation for the throat pressure P₂, accounting for an optional elevation change between the two measurement points. The animated diagram shows particles accelerating through the narrowed throat, with dashed lines marking "Point 1" (inlet) and "Point 2" (throat) where the readouts are taken. If P₂ approaches zero gauge pressure, the tool flags a cavitation-risk warning — a real concern in venturi meters, pump suction lines, and control valves where local pressure can drop below the fluid's vapor pressure and form vapor bubbles that collapse violently downstream.
Venturi meters use this exact relationship to measure flow rate non-invasively: by measuring the pressure difference between the inlet and throat, and knowing the area ratio, the flow rate Q can be back-calculated without any moving parts. The same physics governs pitot-static tubes (which measure V₁ from stagnation vs. static pressure), aspirators and eductors, carburetor venturis, and injector/ejector pumps used to move a secondary fluid using the low pressure created by a high-velocity primary jet.
Bernoulli's equation is a statement of energy conservation: the sum of static pressure energy, kinetic energy, and potential energy per unit volume stays constant along a streamline (for inviscid, incompressible, steady flow). When velocity increases, kinetic energy (½ρV²) increases, so static pressure must decrease to keep the total constant. This is the same principle that generates lift on an airfoil.
Cavitation occurs when local static pressure drops to or below the fluid's vapor pressure, causing vapor bubbles to form. When those bubbles travel to a region of higher pressure downstream, they collapse violently, which can erode pump impellers, valve seats, and pipe walls, and generates significant noise and vibration. Venturi throats, pump suction eyes, and control valve trim are common cavitation locations because they are exactly where velocity is highest and pressure is lowest.
No — this is an ideal (inviscid) Bernoulli calculation with no head loss term. Real venturi meters have a small permanent pressure loss (typically 10–15% of the differential) due to friction and the diverging section's recovery efficiency. For friction-inclusive pipe calculations, see the Pipe Flow & Pressure Drop Simulator, which uses the Darcy-Weisbach equation.
Combining continuity and Bernoulli gives Q = A₂√(2(P₁−P₂)/(ρ(1−(A₂/A₁)²))) — the basis for venturi and orifice flow meters. In this simulator, Q is computed directly from the inlet velocity and area (Q = A₁V₁) rather than back-calculated from ΔP, but the same continuity and Bernoulli relationships tie all four quantities (V₁, V₂, P₁, P₂) together.
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