Question 04 C. A venturi meter is used to measure the flow speed of a fluid in a pipe. The meter is connected between two sections of the pipe (Figure 4.1; the cross-sectional area A of the entrance and exit of the meter matches the pipe's cross-sectional area. Between the entrance and exit, the fluid flows from the pipe with speed V and then through a narrow "throat" of cross-sectional area a with speed v. A manometer connects the wider portion of the meter to the narrower portion. The change in the fluid's speed is accompanied by a change Ap in the fluid's pressure, which causes a height difference h of the liquid in the two 4 arms of the manometer. (Here Ap means pressure in the throat minus pressure in the pipe.) (25 Marks) a. By applying Bernoulli's equation and the equation of continuity to points 1 and 2 in Figure 3.2, show that V 2 Ap pla²-A²) where r is the density of the fluid. b. Suppose that the fluid is fresh water, that the cross-sectional areas are 64 cm in the pipe and 32 cm² in the throat, and that the pressure is 55 kPa in the pipe and 41 kPa in the throat. What is the rate of water flow in cubic meters per second? Meter entrance Pipe Venturi meter Manometer Figure 41 Meter exit Pipe

Question 04 C. A venturi meter is used to measure the flow speed of a fluid in a pipe. The meter is connected between two sections of the pipe (Figure 4.1; the cross-sectional area A of the entrance and exit of the meter matches the pipe's cross-sectional area. Between the entrance and exit, the fluid flows from the pipe with speed V and then through a narrow "throat" of cross-sectional area a with speed v. A manometer connects the wider portion of the meter to the narrower portion. The change in the fluid's speed is accompanied by a change Ap in the fluid's pressure, which causes a height difference h of the liquid in the two 4 arms of the manometer. (Here Ap means pressure in the throat minus pressure in the pipe.) (25 Marks) a. By applying Bernoulli's equation and the equation of continuity to points 1 and 2 in Figure 3.2, show that V 2 Ap pla²-A²) where r is the density of the fluid. b. Suppose that the fluid is fresh water, that the cross-sectional areas are 64 cm in the pipe and 32 cm² in the throat, and that the pressure is 55 kPa in the pipe and 41 kPa in the throat. What is the rate of water flow in cubic meters per second? Meter entrance Pipe Venturi meter Manometer Figure 41 Meter exit Pipe

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter15: Fluids

Section: Chapter Questions

Problem 52PQ: Figure P15.52 shows a Venturi meter, which may be used to measure the speed of a fluid. It consists...

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Figure P15.52 shows a Venturi meter, which may be used to measure the speed of a fluid. It consists of a Venturi tube through which the fluid moves and a manometer used to measure the pressure difference between regions 1 and 2. The fluid of density tube moves from left to right in the Venturi tube. Its speed in region 1 is v1, and its speed in region 2 is v2. The necks cross-sectional area is A2, and the cross-sectional area of the rest of the tube is A1. The manometer contains a fluid of density mano. a. Do you expect the fluid to be higher on the left side or the right side of the manometer? b. The speed v2 of the fluid in the neck comes from measuring the difference between the heights (yR yL) of the fluid on the two sides of manometer. Derive an expression for v2 in terms of (yR yL), A1, A2, tube, and mano. FIGURE P15.52
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