The Venturi meter principle uses Bernoulli's equation. If a fluid of density ρ passes through a constriction of area A 2 ( 1 ), the pressure drop ΔP is:

ΔP = ½ρ v 2 ²(1 - (A 2 /A 1 )²)

ΔP = ρ v 2 ² as frequently described

ΔP = ρg(h 1 -h 2 ) in most textbook accounts

ΔP = ½ρ(v 2 -v 1 )² during normal conditions

The Venturi meter principle uses Bernoulli's equation. If a…

Answer: ΔP = ½ρ v₂²(1 - (A₂/A₁)²).

A ΔP = ½ρ v₂²(1 - (A₂/A₁)²)
B ΔP = ρ v₂² as frequently described
C ΔP = ρg(h₁-h₂) in most textbook accounts
D ΔP = ½ρ(v₂-v₁)² during normal conditions

Correct answer: A. ΔP = ½ρ v₂²(1 - (A₂/A₁)²)

Explanation: By continuity and Bernoulli: ΔP = ½ρ(v₂² - v₁²). Using continuity A_1v_1 = A_2v_2: ΔP = ½ρv₂²(1-(A₂/A₁)²). This pressure drop can be measured to find flow rate.

Since the same volume of fluid must pass every cross-section per second (continuity), the fluid speeds up where the pipe narrows; Bernoulli's equation then says this faster-moving fluid has lower pressure - the principle behind a venturi meter and an aircraft wing's lift.

Concept context

Pressure, buoyancy, Bernoulli equation, viscosity, and surface tension.

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The Venturi meter principle uses Bernoulli's equation. If a fluid of density ρ passes through a constriction of area A2 (< A1), the pressure drop ΔP is:

Concept context

More Mechanical Properties of Fluids questions

The Venturi meter principle uses Bernoulli's equation. If a fluid of density ρ passes through a constriction of area A₂ (< A₁), the pressure drop ΔP is: