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

Question

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.

Answer 1

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