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Given: The viscosity is negligible. Atmospheric pressure is 101300 Pa. Water flows at speed of 5.9...

Given: The viscosity is negligible. Atmospheric pressure is 101300 Pa. Water flows at speed of 5.9 m/s through a horizontal pipe of diameter 3.3 cm. The gauge pressure P1 of the water in the pipe is 1.6 atm. A short segment of the pipe is constricted to a smaller diameter of 2.4 cm.

What is the gauge pressure of the water flowing through the constricted segment? Answer in units of atm.

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Answer #1

The mass flow rate is conserved at both cross sections of the pipe
R = A v
Where is the density ,A is the cross sectional area and v is the velocity of the liquid
We can find the velocity of the water through the constricted segment
A1 v1  = A2 v2
0.033 x 5.9 = 0.024 x v2
v2  = 8.11 m/s
Now we can find the gauge pressure of the water flowing through the constricted segment
P1  + g h + (1/2) v12   = P2  + g h + (1/2) v22
Since the pipe is horizontal, we can neglect the gh term
1 atm = 101300 Pa
1.6 atm = 162080 Pa
162080 + (1/2) 1000 x 5.92   = P2   + (1/2) x 1000 x 8.112
P2   = 146599 Pa
Converting back to atm
P2  = 1.447 atm

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