WEBC07 06/04/2015 21:59:45 Page 399 Suppose the flow rate of an incompressible fluid is

Chapter 7, Problem 7.58

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WEBC07 06/04/2015 21:59:45 Page 399 Suppose the flow rate of an incompressible fluid is to be measured in a venturi meter in which the cross-sectional area at point 1 is four times that at point 2. (a) Derive the relationship between the velocities u1 and u2 at points 1 and 2. (b) Write the Bernoulli equation for the system between points 1 and 2, and use it to prove that to the extent friction is negligible P1 P2 15 V_ 2 2A2 1 where P1 and P2 are the pressures at point 1 and 2, and V_ are the density and volumetric flow rate of the flowing fluid, and A1 is the cross-sectional area of the pipe at point 1. (c) Suppose this meter is used to measure the flow rate of a stream of acetone, using mercury as the manometer fluid, and a manometer reading h 38 cm is recorded. What is the volumetric flow rate of the acetone if the pipe diameter at point 1 is 15 cm? (Recall the differential manometer equation, Equation 3.4-6.)