A pipe tapers out from an initial area A 1 = 3.5x10 -2 m 2 to a final area A 2 t

Question

A pipe tapers out from an initial area A1 = 3.5x10-2 m2 to a final area A2 that is nine times as large over a distance d = 0.31 m. Water enters from the left in a steady volumetric flow of 300 liters/second and initial gauge pressure 11 kPa .

Find the speed v1 of the water just before it enters the flaring part.

Find the area at distance 0.0558 m into the flare.

Find the speed of the water flow at distance 0.0558 into the flare.

By how much does the pressure in the water change between the x = 0.0558 m point and the initial value?

Explanation / Answer

Part A)

Volume Flow Rate = Av

(.3) = (3.5 X 10-2)(v)

v = 8.57 m/s

Part B) Set up a ratio for area change...

9/x = .31/.0558

x = 1.62 times larges

(1.62)(35 X 10-2) = .0567 m2

V = Av

.3 = (.0567)(v)

v = 5.29 m/s

Part C)

From Bernoulli' s Principle...

Delta P = .5p(v22 - v12)

Delta P = .5(1000)(8.572 - 5.292)

Delta = 22730 Pa (which is 22.7 kPa)

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