Answer to Question #184960 in Civil and Environmental Engineering for John Prats

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 cm"^2" , V1 = ? , P1 = 10.2 N/cm²

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


Flow rate formula for equation


A1VI= A2V2

"24\\times V1 = 64 \\times V2"

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

V1=

"\\frac{8V2}{3}"


From Bernoulli's equation


Energy is conserved that is


p1+ "\\frac{1}{2}\\rho V1^2 = p2 + \\frac{1}{2}\\rho V2^2"

"10.2+ \\frac{1}{2}\\ V1^2 = 18.0 + \\frac{1}{2}\\ V2^2"


Substituting V1 from equation 1into equation 2

0.5"\\times (\\frac{8V2}{3})^2 - 0.5 \\ V2^2 = 7.8"

Solving for V2

V2= 3.0594 cm/s


Then V1 ="\\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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