Question

The figure below shows a horizontal pipe with a varying cross section. A liquid with a density of 1.65 g/cm flows from left to right in the pipe, from larger to smaller cross section. The left side's cross-sectional area is 10.0 cm, and while in this side, the speed of the liquid is 2.50 m/s, and the pressure is 1.20 x 105 Pa. The right side's cross sectional area is 3.50 cm? (a) What is the speed (in m/s) of the liquid in the right side (the smaller section)? (Enter your answer to at least three significant figures.) m/s (b) What is the pressure (in Pa) of the liquid in the right side (the smaller section)? - Po

Answer 1

(a)

use continuity equation

A1v1 = A2v2

10e-4 * 2.50 = 3.50e-4 * v2

v2 = 10e-4 * 2.50 / 3.50e-4

v2 = 7.14 m/s

_______

(b)

as the pipe is horizontal, we don't need to worry about height

so,

Bernoulli's equation gives

P1 + 1/2 * $\rho$ * v1 ^ 2 = P2 + 1/2 * $\rho$ * v2 ^ 2

1.20e5 + 1/2 * 1650 * 2.502 = P2 + 1/2 * 1650 * 7.142

solve for P2,

P2 = 8.31e4 Pa