Water is moving with a speed of 2.3 m/s through a perfectly sealed long pipe wit

Question

Water is moving with a speed of 2.3 m/s through a perfectly sealed long pipe with a cross sectional area of 5 cm2. The water descends m as the pipe changes in area to 4cm2. The absolute pressure in the higher section of pipe is 1atm. The pipe is never open to the air.

(a) What is the speed of the water through the lower level of pipe?

(b) What is the absolute pressure in the pipe, at the lower level?

( c) What is the gauge pressure at the higher level?

(d) What volume of water passes through the pipe in 66 minutes?

Explanation / Answer

a)

Using mass conservation law u1 A1 = u2 A2

implies u2 = 11.5/4 = 2.875 m/s

b) using bernoullis equation

the altitude gradient needs to be added to the bernoulli equation..

p = p abs - 1/2*density * v^2 + density*g*h

p = 10^5 - 500*2.875^2 - 1000*9.8*0.89 = 0.871 atm

c) gauge pressure= 1/2*density*v^2 = 500*2.3^2 = 2645 Pa

d) volume = A*v*t = 66*60*2.3* 5*10^-4 = 4.554 cubic metres of water will flow

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