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 1.5atm and the flow speed is 12.0 m/s. At the top of the hill, the water has pressure of 1.30 atm in the pipe and flows with a speed of 7.0 m/s.

a) What is the height of the hill? (Assume the pipe is sealed and completely filled with imcompressible water, but that its diameter varies.) Show your work.

b) At the bottome of the hill, the pipe's diameter is 35.0 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

let,

pressure, P1=1.5 atm

pressure, P2=1.3 atm

flow speed, v1=12 m/sec

flow speed, v2=7 m/sec

a)

from the Bernoulli's equation,

P+(1/2*rho*v^2)+(rho*g*h)=constant

=====>

P1+(1/2*rho*v1^2)+rho*g*h1=P2+(1/2*rho*v2^2)+rho*g*h2

(P1-P2)+1/2*rho*(v1^2-V2^2)+rho*g*(h1-h2)=0

(1.5-1.3)*1.01*10^5 +1/2*1000*(12^2-7^2)+1000*9.8*(h)=0

====>

h1-h2=-6.91 m

===>

height of the pipe, h=6.91 m

b)

let,

diameter, d1=35cm

use,

A1*v1=A2*v2

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

(r1^2)*v1=(r2^2)*v2

v1/v2=(r2/r1)^2

v1/v2=(d2/d1)^2

12/7=(d2/0.35)^2

===>

d2=0.458 m

or

d2=45.8 cm

diameter, d2=45.8 cm

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