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 (Fig. 14-43); 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 ?p in the fluid’s pressure, which causes a height difference h of the liquid in the two arms of the manometer. (Here ?p means pressure in the throat minus pressure in the pipe.) (a) By applying Bernoulli’s equation and the equation of continuity to points 1 and 2 in Fig. 14-43, show that where r is the density of the fluid. (b) Suppose that the fluid is fresh water, that the cross-sectional areas are 60 cm2 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? MeterMeterentranceVenturi meterexitVAAаV2Pipe1Pipeh- ManometerFigure 14-43 Problems 59 and 60. 59 A venturi meter is used to measure the flow speed of a fluidin a pipe. The meter is connected between two sections of thepipe (Fig. 14-43); the cross-sectional area A of the entrance andexit of the meter matches the pipe's cross-sectional area.Between the entrance and exit, the fluid flows from the pipewith speed V and then through a narrow "throat" of cross-sectional area a with speed v. A manometer connects the widerportion of the meter to the narrower portion. The change in thefluid's speed is accompanied by a change Ap in the fluid'spressure, which causes a height difference h of the liquid in thetwo arms of the manometer. (Here Ap means pressure in thethroat minus pressure in the pipe.) (a) By applying Bernoulli'sequation and the equation of continuity to points 1 and 2 inFig. 14-43, show that2a² ApV =p(a? – A?)'where p is the density of the fluid. (b) Suppose that the fluid isfresh water, that the cross-sectional areas are 60 cm? in the pipeand 32 cm? in the throat, and that the pressure is 55 kPa in thepipe and 41 kPa in the throat. What is the rate of water flow incubic meters per second?

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Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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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 (Fig. 14-43); 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 ?p in the fluid’s pressure, which causes a height difference h of the liquid in the two arms of the manometer. (Here ?p means pressure in the throat minus pressure in the pipe.) (a) By applying Bernoulli’s equation and the equation of continuity to points 1 and 2 in Fig. 14-43, show that

where r is the density of the fluid. (b) Suppose that the fluid is fresh water, that the cross-sectional areas are 60 cm2 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
Meter
entrance
Venturi meter
exit
V
A
A
а
V
2
Pipe
1
Pipe
h
- Manometer
Figure 14-43 Problems 59 and 60.

59 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 (Fig. 14-43); 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 arms of the manometer. (Here Ap means pressure in the
throat minus pressure in the pipe.) (a) By applying Bernoulli's
equation and the equation of continuity to points 1 and 2 in
Fig. 14-43, show that
2a² Ap
V =
p(a? – A?)'
where p is the density of the fluid. (b) Suppose that the fluid is
fresh water, that the cross-sectional areas are 60 cm? in the pipe
and 32 cm? 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?

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