Question

# 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.

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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