Problem 15.61 Unfiltered olive oil must flow at a minimum speed of 3.0 m/s to pr

Question

Problem 15.61

Unfiltered olive oil must flow at a minimum speed of 3.0 m/s to prevent settling of debris in a pipe. The oil leaves a pump at a pressure of 86 kPa through a pipe of radius 9.3 mm. 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/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.

Explanation / Answer

Given that,

v2 = 3 m/s

P1 = 86000 Pa

P2 = 101325 Pa

r1 = 9.3*10^(-3) m

(A)

Apply bernaolli's equation,

(1/2)P1v1^2 = (1/2)P2v2^2

86000 * v1^2 = 101325 * 3^2

v1 = 3.25 m/s

speed of the oil as it leaves the pump = 3.25 m/s

(B)

From equation of continuity,

A1*v1 = A2*v2

pi*r1^2 * v1 = pi*r2^2 * v2

(9.3*10^(-3))^2 * (3.25)^2 = r2^2 * 3^2

r2 = 10.09 mm

radius of the horizontal pipe = 10.09 mm

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