The Venturi tube shown in the figure below may be used as a fluid flowmeter. Sup

Question

The Venturi tube shown in the figure below may be used as a fluid flowmeter. Suppose the device is used at a service station to measure the flow rate of gasoline (? =

The Venturi tube shown in the figure below may be used as a fluid flowmeter. Suppose the device is used at a service station to measure the flow rate of gasoline (? = 7.00 102 kg/m3) through a hose having an outlet radius of 1.45 cm. The difference in pressure is measured to be P1 ? P2 = 1.70 kPa and the radius of the inlet tube to the meter is 2.90 cm. Find the speed of the gasoline as it leaves the hose. m/s Find the fluid flow rate in cubic meters per second. m3/s

Explanation / Answer

P1 + 1/2*rho*V1^2 = P2 + 1/2*rho*V2^2

P1 - P2 = 1/2*rho*(V2^2 - V1^2)

1.7*10^3 = 1/2*7*10^2 * (V2^2 - V1^2)

V2^2 - V1^2 = 4.857......................1

Q = A1*V1 = A2*V2

Q = 3.14* r1^2 *V1 = 3.14*r2^2 *V2

V1 = V2*(r2/r1)^2

V1 = V2*(1.45/2.9)^2

V1 = V2*0.25

Putting it in eqn 1

V2^2 - (V2*0.25)^2 = 4.857

Solving, V2 = 2.276 m/s

b)

Q = A2*V2

= 3.14*r2 ^2 *2

= 3.14*(1.45*10^-2)^2 *2.276

= 0.0015 m^3/s

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