Question

Unfiltered olive oil must flow at a minimum speed of 3.0 m/sm/s to prevent settling of debris in a pipe. The oil leaves a pump at a pressure of 91 kPakPa through a pipe of radius 9.2 mmmm. It then enters a horizontal pipe at atmospheric pressure. Ignore the effects of viscosity.

Part A

What is the speed of the oil as it leaves the pump if it flows at 3.0 m/sm/s in the horizontal pipe?

Express your answer to two significant figures and include appropriate units.

Part B
What is the radius of the horizontal pipe?

Express your answer to two significant figures and include appropriate units.

Answer 1

(a)

as pipe is horizontal , Bernoulli's equation is

1/2v₁² + p1 = p2 + 1/2v₂²

1/2v₁² = p2 + 1/2v₂² - p1

1/2v₁² = 101e3 + 1/2 * * 3² - 91e3

1/2v₁² = 10000 + 4.5

density of olive oil is 918 kg/m³

so,

v1 = 5.5 m/s

_________________________

(b)

use continuity

A1v1 = A2v2

r1² v1 = r2² v2

9.2e-3² * 5.548 = r2² * 3

so,

r2 = 12.5 mm or 13 mm