iPadges 10:14 AM @55%.D Homework 122 COhttps://www.webassign.netweb Student/Assi

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iPadges 10:14 AM @55%.D Homework 122 COhttps://www.webassign.netweb Student/Assignment Responses/submit?depe13464838 -12 points OSColPhys1 12.P.021.WA. 05 Submissions U My Notes Ask Your Teacher A refinery uses a Venturi tube like the one shown in the figure to monitor the flow of gasoline (p 7.00 x 102 kg/m3) through a hose. The inlet radius of the Venturi tube is 2.40 cm, the outlet radius is 1.60 cm, and the difference in pressure measured by the two gauges is P1 P21.20 kPa. Pi P2 (a) Determine the speed of the gas as it leaves the Venturi tube m/s (b) Determine the volume flow rate of the gasoline. m3/s Supporting Materials Physical Constants

Explanation / Answer

(a) Assuming frictionless and incompressible flow you can apply Bernoulli's principle:
(p/) + gz + (1/2)v² = constant
=> (p/) + gz + (1/2)v² = (p/) + gz + (1/2)v²
Since inlet and outlet are the same height, i.e. z=z
=> v² - v² = 2(p - p)/

For an incompressible fluid the volumetric flow rate through each cross-section is the same:
Q = Q
volumetric flow rate equals velocity time cross-sectional area
vA = vA
<=> vr² = vr²
=> v = v(r/r)²

Hence, v² - (v(r/r)²)² = 2(p - p)/
<=> v²(1 - (r/r)) = 2(p - p)/
=> v = [ 2(p - p) / ((1 - (r/r))) ]
= [ 2*1200Pa / (700kg/m³(1 - (1.6/2.4))) = 2.067 m/s

(b) Q = vr²
= 2.067m/s (0.024m)²
= 3.74×10³ m³/s

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