When using a Venturi meter, a decrease in the cross-sectional area causes:

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  1. an increase in static pressure
  2. no change in velocity
  3. a decrease in static pressure
  4. an increase in fluid density

Answer (Detailed Solution Below)

Option 3 : a decrease in static pressure
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Explanation:

Venturi Meter:

  • A Venturi meter is a device used for measuring the flow rate of a fluid in a pipeline. It works on the principle of Bernoulli's equation, which states that in a steady, incompressible flow, the sum of the pressure energy, kinetic energy, and potential energy per unit volume is constant along a streamline. The Venturi meter consists of three main sections: the converging section, the throat (narrowest section), and the diverging section.
  • When fluid flows through the Venturi meter, it experiences a change in velocity and pressure due to the varying cross-sectional area. As the fluid enters the converging section, the cross-sectional area decreases, causing the velocity of the fluid to increase. According to Bernoulli's principle, an increase in velocity is accompanied by a decrease in static pressure. At the throat, where the cross-sectional area is smallest, the velocity is at its maximum, and the static pressure is at its minimum. As the fluid moves into the diverging section, the cross-sectional area increases, the velocity decreases, and the static pressure recovers.

A decrease in the cross-sectional area causes a decrease in static pressure.

  • When the cross-sectional area decreases in the Venturi meter, the velocity of the fluid increases to conserve the mass flow rate. As velocity increases, the static pressure decreases to maintain the conservation of energy, as described by Bernoulli's equation. This phenomenon is fundamental to the working of the Venturi meter and is the reason it is used to measure flow rates by observing the pressure difference between the wide and narrow sections of the meter.
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