Correct Answer - Option 3 : Bernoulli’s principle
CONCEPT:
Venturi-meter:
- The Venturi-meter is a device to measure the flow speed of the incompressible fluid.
- Venturimeter works on the principle of Bernoulli’s equation.
- It consists of a tube with a broad diameter and a small constriction at the middle as shown in the figure.
- A manometer in the form of a U-tube is also attached to it, with one arm at the broad neck point of the tube and the other at constriction as shown in the figure.
- By the continuity equation,
⇒ Av1 = av2
- By Bernoulli's equation, the pressure difference between the broad neck and the narrow neck of a venturi-meter is given as,
\(\Rightarrow P_1-P_2=\frac{1}{2}ρ v_1^2\left [ \left ( \frac{A}{a} \right )^2-1 \right ]\)
- The speed of the fluid at the broad neck is given as,
\(\Rightarrow v_1=\sqrt{\left ( \frac{2ρ_m gh}{ρ} \right )}\left [ \left ( \frac{A}{a} \right )^2-1 \right ]^{-1/2}\)
Where A = cross-sectional area at the broad neck, a = cross-sectional area at the narrow neck, v1 = speed of the fluid at the broad neck, v2 = speed of the fluid at the narrow neck, ρ = density of the fluid, ρm = density of the fluid in the manometer, h = difference in the height of the manometer liquid column, and g = gravitational acceleration
EXPLANATION:
- The Venturi-meter is a device to measure the flow speed of the incompressible fluid.
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Venturimeter works on the principle of Bernoulli’s equation. Hence, option 3 is correct.
Applications of venturi-meter:
- The carburetor of an automobile has a Venturi channel (nozzle) through which air flows at a large speed. The pressure is then lowered at the narrow neck and the petrol (gasoline) is sucked up in the chamber to provide the correct mixture of air to fuel necessary for combustion.
- Filter pumps or aspirators, Bunsen burner, atomizers, and sprayers are used for perfumes or to spray insecticides.
