A venturi meter is used to measure the flow speed of a fluid in a pipe. The mete

Question

A venturi meter is used to measure the flow speed of a fluid in a pipe. The meter s connected between two sections of the pipe (the figure); 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 tip in the fluid?s pressure, which causes a height difference h of the liquid in the two arms of the manometer. (Here tip means pressure in the throat minus pressure in the pipe.) Let A equal 6a. Suppose the pressure p. at A is 2.7 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 7.5 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.

Explanation / Answer

using venturi meter principle (which is a combination of both bernoulli' principle and continuity principle),

p1-p2=density*(v2^2-v1^2)/2...(1)

given that p1=2.7 atm
p2=0 atm

density=1000 kg/m^3

using continuity principle, v1*A=v2*a

given that, A=6*a

==> v1*6=v2

substituting in the equation 1,

35*v1^2*0.5*1000=2.7*101325 (using 1 atm=101325 N/m^2)

we get v1=3.9539 m/s

then v2=6*v1=23.723 m/s

hence,

a) speed V at A is v1=3.9539 m/s

b) speed v at a is v2=23.723 m/s

c)flow rate=speed*area=0.0175 m^3/sec

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.