A Venturi tube may be used as a fluid flowmeter (see Fig,...

A Venturi tube may be used as a fluid flowmeter (see Fig, $14.19 ) .$ Taking the difference in pressure as $P_{1}-P_{2}=$ 21.0 $\mathrm{kPa}$ , find the fluid flow rate in cubic meters per second given that the radius of the outlet tube is 1.00 $\mathrm{cm}$ , the radius of the inlet tube is $2.00 \mathrm{cm},$ and the fluid is gasoline $\left(\rho=700 \mathrm{kg} / \mathrm{m}^{3}\right) .$

Key Concepts

Volumetric Flow Rate Calculation

The volumetric flow rate is calculated by combining the relationships from the continuity equation and Bernoulli's principle. This involves using the measured pressure difference between the inlet and throat of the Venturi meter and the cross-sectional areas of those sections. Calculating the flow rate typically requires manipulating these equations to solve for the fluid velocity and then multiplying by the area of the section where the flow rate is desired.

Continuity Equation

The continuity equation arises from the conservation of mass in incompressible fluid flow, meaning that the mass flow rate must be constant along a streamline. In practice, it relates the cross-sectional area of the flow to the velocity of the fluid. For a Venturi meter, the continuity equation allows one to determine the change in velocity between the wider inlet section and the narrower throat, which is essential for calculating the volumetric flow rate.

Bernoulli's Principle

Bernoulli's principle is a fundamental principle in fluid dynamics that states that in a streamline flow, the sum of the pressure energy, kinetic energy per unit volume, and potential energy per unit volume remains constant. In the context of a Venturi meter, this principle explains how an increase in fluid velocity in the constricted section results in a corresponding drop in pressure, which is critical for flow measurement.

Venturi Meter

A Venturi meter is a flow measurement device that uses a tube with a constricted throat. As fluid flows through the tube, the velocity increases in the constricted section, leading to a drop in pressure. This pressure differential is then used to determine the flow rate of the fluid. The Venturi meter is particularly effective for measuring the flow of liquids and gases in pipelines.

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