Question #184960

Water flows through a venturi meter. At the constricted section where the area is 24 cm³, the pressure is 10.2 N/cm², and at the section where the area is 64 cm², the pressure is 18.0 N/cm². Determine the velocities of water in the larger and smaller pipes and the rate of flow.


1
Expert's answer
2021-05-07T08:12:23-0400

The factors that are to be considered are the differential head and the density of fluid that is constant. The pipe is assumed to frictionless.

A1 = 24 cm2^2 , V1 = ? , P1 = 10.2 N/cm²

A2= 64 cm2^2 , V2 = ? , P2= 18.0 N/cm²


Flow rate formula for equation


A1VI= A2V2

24×V1=64×V224\times V1 = 64 \times V2

V1 = 64×V224\frac {64 \times V2 }{24} = equation 1

V1=

8V23\frac{8V2}{3}


From Bernoulli's equation


Energy is conserved that is


p1+ 12ρV12=p2+12ρV22\frac{1}{2}\rho V1^2 = p2 + \frac{1}{2}\rho V2^2

10.2+12 V12=18.0+12 V2210.2+ \frac{1}{2}\ V1^2 = 18.0 + \frac{1}{2}\ V2^2


Substituting V1 from equation 1into equation 2

0.5×(8V23)20.5 V22=7.8\times (\frac{8V2}{3})^2 - 0.5 \ V2^2 = 7.8

Solving for V2

V2= 3.0594 cm/s


Then V1 =64×V224=64×3.059424=8.1584m/s\frac {64 \times V2 }{24} = \frac {64 \times 3.0594 }{24} = 8.1584 m/s


V1 = 8.1584 cm/s , V2 = 3.0594 cm/s



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