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 (? = 7.70*10^2 kg/m3) through a hose having an outlet radius of 1.87 cm. The difference in pressure is measured to be P1 ? P2 = 1.20 kPa and the radius of the inlet tube to the meter is 3.74 cm.

A) Find the speed of the gasoline as it leaves the hose. (in m/s)

B) Find the fluid flow rate in cubit meters per second.

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 (p = 7.70 x 102 kg/m3) through a hose having an outlet radius of 1.87 cm. The difference in pressure is measured to be P1 -P2 = 1.20 kPa and the radius of the inlet tube to the meter is 3.74 cm. Pi P2 (a) Find the speed of the gasoline as it leaves the hose. 577 X m/s (b) Find the fluid flow rate in cubic meters per second. m3/s

Explanation / Answer

here,

density , p = 7.7 * 10^2 kg/m^3

outlet radius , ro = 0.0187 cm

P1 - P2 = 1200 Pa

radius of inlet ,ri = 0.0374 m

A)

let the speeds be vi and vo

using Bernouli's theorm

P1 - P2 = 0.5 * p * ( vi^2 - vo^2)

1200 = 0.5 * 770 * ( v1^2 - vo^2 ) ....(1)

and

using the equation of continuity

Area1 * vi = area2 * vo

pi * 0.0374^2 * vi = pi * 0.0187^2 * vo ....(2)

from (1) and (2)

vo = 1.82 m/s

vi = 0.46 m/s

the speed of gasoline as it leaves the hose is 1.82 m/s

B)

the fluid flow rate in cubit meters per second, V = area1 * vo

V = pi * 0.0187^2 * 1.82

V = 2 * 10^-3 m^3/s

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