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 (? =7.00 102 kg/m3) through a hose having an outlet radius of 2.86 cm. The difference in pressure is measured to be P1 - P2 = 1.40 kPa and the radius of the inlet tube tothe meter is 1.43 cm.

a) Find the speed of the gasoline as it leaves the hose.

Answer 1

Outlet radius R = 2.86 cmmInlet radius r = 1.43 cmFrom equation of continuity ,Av = A 'v'(πr² v ) = (πR ² v ' )v = ( R / r ) ² v '= 4v 'Pressure difference dP = 1.4kPa= 1400 PaWe know from bernoulli's theorem,dP = ( 1/ 2) ρ[ v ² - v ' ² ]Where ρ = density of gasline= 700 kg / m ³Substitute values we get1400 = 350 [ 16 v' ² - v ' ² ]= 350 x 15 v' ²v ' = 0.5163 m / s