Flying Circus of Physics 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 (see the figure below); 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 4p means pressure in the throat minus pressure in the pipe.) Let A equal 3-a. Suppose the pressure p₁ at A is 3.0 atm. Compute the values of (a) the speed V at A and (b) the speed v at a that make the pressure p2 at a equal to zero. (c) Compute the corresponding volume flow rate if the diameter at A is 4.5 cm. The phenomenon that occurs at a when p2 falls to nearly zero is known as cavitation. Please assume that the fluid is water. The water vaporizes into small bubbles. Meter entrance V Pipe A 1 Venturi meter V a Manometer A Meter exit Pipe

Flying Circus of Physics 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 (see the figure below); 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 4p means pressure in the throat minus pressure in the pipe.) Let A equal 3-a. Suppose the pressure p₁ at A is 3.0 atm. Compute the values of (a) the speed V at A and (b) the speed v at a that make the pressure p2 at a equal to zero. (c) Compute the corresponding volume flow rate if the diameter at A is 4.5 cm. The phenomenon that occurs at a when p2 falls to nearly zero is known as cavitation. Please assume that the fluid is water. The water vaporizes into small bubbles. Meter entrance V Pipe A 1 Venturi meter V a Manometer A Meter exit Pipe

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter12: Fluid Dynamics And Its Biological And Medical Applications

Section: Chapter Questions

Problem 2CQ: Many figures in the text show streamlines. Explain why fluid velocity is greatest where streamlines...

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Question

Flying Circus of Physics
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 (see the
figure below); 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.) Let A equal 3-a. Suppose the pressure p₁ at A is 3.0 atm. Compute the values of (a)
the speed V at A and (b) the speed v at a that make the pressure p2 at a equal to zero. (c) Compute the corresponding volume flow rate
if the diameter at A is 4.5 cm. The phenomenon that occurs at a when p2 falls to nearly zero is known as cavitation. Please assume that
the fluid is water. The water vaporizes into small bubbles.
Meter
entrance
V
Pipe
h
Venturi meter
2
Manometer
Meter
exit
Pipe

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