The Venturi tube discussed in Example 14.8 and shown in Figure P 14.47 may be used as a fluid fl

step 1 In this question we have given a venturi meter and it is used to measure the flow rate from the

The Venturi tube discussed in Example 14.8 and shown in...

The Venturi tube discussed in Example 14.8 and shown in Figure $\mathrm{P} 14.47$ may be used as a fluid flowmeter. Suppose the device is used at a service station to measure the flow rate of gasoline $\left(\rho=7.00 \times 10^{2} \mathrm{kg} / \mathrm{m}^{3}\right)$ through a hose having an outlet radius of $1.20 \mathrm{cm} .$ If the difference in pressure is measured to be $P_{1}-P_{2}=1.20 \mathrm{kPa}$ and the radius of the inlet tube to the meter is $2.40 \mathrm{cm},$ find ( a ) the speed of the gasoline as it leaves the hose and (b) the fluid flow rate in cubic meters per second.

The Venturi tube discussed in Example 14.8 and shown in Figure $\mathrm{P} 14.47$ may be used as a fluid flowmeter. Suppose the device is used at a service station to measure the flow rate of gasoline $\left(\rho=7.00 \times 10^{2} \mathrm{kg} / \mathrm{m}^{3}\right)$ through a hose having an outlet radius of $1.20 \mathrm{cm} .$ If the difference in pressure is measured to be $P_{1}-P_{2}=1.20 \mathrm{kPa}$ and the radius of the inlet tube to the meter is $2.40 \mathrm{cm},$ find ( a ) the speed of
the gasoline as it leaves the hose and (b) the fluid flow rate in cubic meters per second.

Key Concepts

Bernoulli's Principle

Bernoulli's Principle relates the pressure, velocity, and elevation along a streamline in a flowing, incompressible fluid. It explains how an increase in the fluid speed results in a decrease in pressure or potential energy, and is fundamental in deriving the relationship between pressure differences and velocity changes in devices like Venturi meters.

Continuity Equation

The Continuity Equation embodies the principle of conservation of mass for an incompressible fluid. It states that the mass flow rate must remain constant from one cross-section of a flow to another, meaning that the product of the cross-sectional area and the fluid velocity is constant along the flow. This is used to relate velocities at different sections of a flowmeter with varying diameters.

Venturi Meter

A Venturi Meter is a device that measures the flow rate of a fluid through a conduit by introducing a constriction in the flow path. The resulting pressure drop between the wider section and the narrow throat, as explained by Bernoulli's Principle and the Continuity Equation, is used to calculate the fluid's velocity and, subsequently, the volumetric flow rate.

Flow Rate Calculation

Flow rate calculation involves determining the volumetric amount of fluid passing through a cross-section per unit time. This is typically calculated by multiplying the fluid velocity by the cross-sectional area of the flow at that section. In the context of flowmeters and Venturi tubes, this calculation helps to quantify the fluid delivery rate based on measured velocities or pressure differentials.

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