Question

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.

Name: the venturi tube discussed in example 148 and shown in figure mathrmp 1447 may be used as a fluid flowmeter suppose the device is used at a service station to measure the flow rate of gasoline leftr 2
Uploaded: 2021-08-26T00:40:59-08:00
Duration: 4 min 36 s
Channel: Surendra Kumar
Description: the venturi tube discussed in example 148 and shown in figure mathrmp 1447 may be used as a fluid flowmeter suppose the device is used at a service station to measure the flow rate of gasoline leftr 2

          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.

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Physics for Scientists and Engineers with Modern Physics

Raymond A. Serway, John W. Jewett, Jr. 8th Edition

Chapter 14

Instant Answer

Solved by Expert Surendra Kumar

08/26/2021

Step 1

Also, since the fluid is incompressible, the density $\rho$ is constant. Therefore, the equation simplifies to: $$P_1 + \frac{1}{2}\rho v_1^2 = P_2 + \frac{1}{2}\rho v_2^2$$ $$\frac{1}{2}\rho v_1^2 = P_2 - P_1 + \frac{1}{2}\rho v_2^2$$ $$v_1^2 = \frac{2}{\rho}(P_2 Show more…

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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.