Question

The inside diameters of the larger portions of the horizontal pipe in Figure P9.47 are 2.60 cm. Water flows to the right at a rate of 2.10 ✕ 10-4 m3/s. Determine the inside diameter of the constriction.

http://www.webassign.net/sf/p9_47.gif

Answer 1

This device measures flow using the pressure difference due to velocity, it's a Venturi meter.

p + (1/2) rho v^2 + rho g h = constant Bernoulli

p1 + (1/2) rho v1^2 = p2 + (1/2) rho v2^2, as

h is same height for both
p2 - p1 = pressure difference = - (1/2 rho (v2^s2 - v1^2)

the pressure difference from the figure is rho g (0.05 m - 010 m)

where rho = water density 1000kg/m3 and g = 9.8 N/kg

from the volume flow Q = v1 A1, you can get v1.

from the pressure difference, you can get v2

from v2, you can get the area of the constriction, A2

from Q = A2 v2, you can get A2 which is the area of a circle of diameter
(pi/4) d2^2. d2 is your answer.

chug away!

Answer 2

Thank you!!