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 0.89m 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) According to continuity

A1*v1 = A2*v2

5*2.3 = 4* v2

v2 = 2.875 m/s

2) P/rho + g*z + v^2/2 = constant

so

P1/rho + g*z1 + v1^2/2 = P1/2 + g*z2 + v2^2/2

P1 = 1 atm = 1.01325*10^5 N/m^2

rho = 1000 kg/m^3

z1 = 0.89

z2 = 0

v1 = 2.3

v2 = 2.875

P2/rho = 101.325 + 9.81*0.89 + (2.3^2 - 2.875^2)/2 = 108.568

P2 = 1.08568 *10^5 N/m^2

P2 = 1.08568/1.01325 atm = 1.07148 atm

3) gauge pressure = absolute pressure - atmospheric pressure = 1 atm - 1 atm = 0

4) Q = A*v

Volume = Q*t

Q = (5*10^-4)*(2.3)

t = 66*60

V = (5*10^-4)*(2.3)*66*60 = 4.554 m^3 = 4554 litres

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