A Venturi flow meter is used to measure the the flow velocity of a water main. The water main has a diameter of 30.0 cm, and the constriction has a diameter of 10.0 cm. The two vertical pipes are open at the top, and the difference in water level between them is 3.0 m.

Question

Find the velocity, vm (in m/s)of the water in the main.

The volumetric flow rate, Q (in m3/s) of the water in the main.

Answer 1

volume flow is the same in the big section as the small.

pi Rbig^2 Vbig = pi Rsmall^2 Vsmall
so
Vsmall = Vbig (15^2/5^2) = 9 Vbig

then Bernoulli

(1/2)rho Vsmall^2 = (1/2) rho Vbig^2 +rho g h

2 g h = (Vsmall^2 - Vbig^2)
2 (9.81)(3) = 81Vbig^2 - 1 Vbig^2
= 80 Vbig^2
so
Vbig^2 = .736 m^2/s^2
Vbig = .858 m/s in big main

Q = pi (.15^2) .858 = .06 m^3/sec

Answer 2

thanks

Answer 3

I am not getting the correct answer, can you plz explain a bit better? Thankx