   Chapter 9, Problem 48P

Chapter
Section
Textbook Problem

The Venturi tube shown in Figure P9.48 may be used as a fluid flowmeter. Suppose the device is used at a service station to measure the flow rate of gasoline (ρ = 7.00 × 102 kg/m2) through a nose having an outlet radius of 1.20 cm. If the difference in pressure is measured to be P1, − P2; = 1.20 kPa and the radius of the inlet tube to the meter is 2.40 cm, find (a) the speed of the gasoline as it leaves the hose and (b) the fluid flow rate in cubic meters per second. Figure P9.48

(a)

To determine
The speed of the gasoline as it leaves the hose.

Explanation
Bernoulli’s equation is used for the speed of the flow speed of the gasoline in the venture meter that is P1+(1/2)ρv12+ρgh1=P2+(1/2)ρv22+ρgh2 where h1=h2 and v22v12=2(P1P2)/ρ . From the relation of continuity the speed of gasoline at the outlet of the venture meter is A1v1=A2v2v2=(r1/r2)2v1=(r1/r2)2v222(P1P2)ρ and its reduced form is v2=2(P1P2)/[11/(r1/r2)4]ρ .

Given info: The pressure difference is 1.20×103Pa , density of gasoline is 7.00×102kg/m3 , radius of the inlet is 2.40cm , and radius of outlet is 1

(b)

To determine
The fluid flow rate in cubic meters per second.

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