⛰️ 2D Bernoulli's Principle — Venturi Hill Pipe
A pipe that both narrows and climbs at the same point. Continuity (A₁v₁ = A₂v₂) sets the velocity from the cross-section alone; the full Bernoulli equation P + ½ρv² + ρgh = const then sets the pressure from velocity and elevation together.
Flow
Results
Fluid
How it works
This pipe both narrows and rises to a hill at the same point — a Venturi throat sitting at elevation Δh above the inlet. The continuity equation A₁v₁ = A₂v₂ fixes velocity from cross-section alone, independent of height. The full Bernoulli equation P + ½ρv² + ρgh = const then combines two effects into the pressure drop: the venturi speed-up (−½ρ(v₂²−v₁²)) and the climb (−ρgΔh). Both terms lower pressure at the throat, so raising the hill or tightening the constriction both push pressure down independently.
Set Δh to 0 to isolate the pure venturi effect (flat pipe); raise it to see the hydrostatic term add on top, exactly the way a real elevated pipeline or an aircraft's climbing airspeed indicator must account for both cross-section and altitude.