Bernoulli & VenturiJEE Main

Concept

For an ideal fluid, squeezing the pipe speeds the flow (continuity), and faster flow has lower pressure (Bernoulli). A venturi meter uses the pressure drop at a throat to measure flow rate.

Key formula

Derivation

Continuity (mass conservation) for an incompressible fluid: the same volume per second passes every section, so $A_1v_1 = A_2v_2$ and the throat speed is $v_2 = v_1 A_1/A_2$.

Bernoulli's equation (energy conservation along a streamline, horizontal pipe) then gives the pressure drop $\Delta P = P_1 - P_2 = \tfrac12\rho(v_2^2 - v_1^2)$ — positive, so pressure is lowest where the pipe is narrowest.

Scenarios to explore

• Bernoulli & Venturi — Continuity and the pressure drop at a throat.

Real-world applications

• Venturi & Pitot tubes for measuring flow speed.
• Aerofoil lift and the curve of a spinning ball (Magnus effect).
• Carburettors and atomisers (spray bottles).

JEE exam tips

• Combine continuity and Bernoulli to eliminate $v_2$ in venturi problems.
• Add $\rho g h$ terms when the pipe changes height.

Common mistakes

• Thinking the narrow section has higher pressure — it is lower.
• Forgetting to convert areas from cm² to m² in SI.
• Applying Bernoulli across a region with friction or turbulence.

Exam traps to avoid

• Bernoulli assumes steady, non-viscous, incompressible, streamline flow.
• A wider pipe carries the same volume flow but at a lower speed and higher pressure.