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 times 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. Find the fluid flow rate in cubic meters per second.

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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