A sealed, pressurized pipe carries fresh water up a small hill. At the bottom of

Question

A sealed, pressurized pipe carries fresh water up a small hill. At the bottom of the hill, the pressure in the pipe is 1.60 atm and the flow speed is 12.0 m/s. At the top of the hill, the water has a pressure of 1.30 atm in the pipe and flows with a speed of 8.00 m/s. a. What is the height of the hill? (Assume the pipe is sealed and completely filled with incompressible water, but that its diameter varies.) Show your work. b. At the bottom of the hill, the pipe's diameter is 30.0 cm. Find its diameter at the top of the hill. (Assume that the pipe's cross-section is everywhere circular, and that the water is incompressible.)

Explanation / Answer

P1 = 1.6 atm , v1 = 12 m/s

P2 = 1.3 atm , v2 = 8 m/s

1 atm = 101325 Pa

desity of water p= 1000 kg/m^3

(a) from Bernoullis principle

P1 +0.5pv1^2 +pgh1 = P2 +0.5pv2^2 +pgh2

h1 = 0

1.6*101325 +0.5*1000*12*12 +0 = 1.3*101325 +0.5*1000*8*8 +1000*9.8*h

h = 7.18 m

(b) d1 = 30 cm ,

from equation of continuity

A1v1 = A2v2

(pi*d1^2/4)v1 = (pi*d2^2/4)v2

(30*30)*12 = (d2)^2*8

d2 = 36.74 cm

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