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 (ñ = 7.00 102 kg/m3) through a hose having an outlet radius of 2.72 cm. The difference in pressure is measured to be P1 − P2 = 2.00 kPa and the radius of the inlet tube to the meter is 1.36 cm.

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 (ñ = 7.00 102 kg/m3) through a hose having an outlet radius of 2.72 cm. The difference in pressure is measured to be P1 − P2 = 2.00 kPa and the radius of the inlet tube to the meter is 1.36 cm. 
(a) Find the speed of the gasoline as it leaves the hose.
 m/s

(b) Find the fluid flow rate in cubic meters per second.
 m3/s

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Anonymous · Answer

Try to use P2-P1 = ρ/2(v1^2-v2^2)
Derived from P1 + 1/2ρv1^2 = P2 + 1/2ρv2^2

Then A1V1 = A2V2 is from continuity and can be expressed V1 = A2V2/A1

You get the equation P2 - P1 = ρ/2((A2V2/A1)^2 - V2^2) via substitution

And then simplify to 2(P2-P1)/ρ = A2V2/A1 - V2^2

Plug in and solve

McKenna · Answer

7.6