A liquid of density 1390 kg/m3 flows steadily through a pipe of varying diameter and height. At Location 1 along the pipe, the flow speed is 9.45 m/s and the pipe diameter d1 is 10.3 cm. At Location 2, the pipe diameter d2 is 14.9 cm. At Location 1, the pipe is Δy=9.91 m higher than it is at Location 2. Ignoring viscosity, calculate the difference ΔP between the fluid pressure at Location 2 and the fluid pressure at Location 1.
Gravitational acceleration = g = 9.81 m/s2
Density of liquid = = 1390
kg/m3
Pressure of the liquid at point 1 = P1
Diameter of pipe at point 1 = D1 = 10.3 cm = 0.103 m
Cross-sectional area of pipe at point 1 = A1 =
D12/4
Speed of flow of liquid at point 1 = V1 = 9.45 m/s
Height of point 1 compared to point 2 = Y = 9.91 m
Pressure of the liquid at point 2 = P2
Diameter of pipe at point 2 = D2 = 14.9 cm = 0.149 m
Cross-sectional area of pipe at point 2 = A2 =
D22/4
Speed of flow of liquid at point 2 = V2
Difference of fluid pressure between point 2 and point 1 =
P = P2
- P1
By continuity equation,
A1V1 = A2V2
(D12/4)V1
= (
D22/4)V2
D12V1 = D22V2
(0.103)2(9.45) = (0.149)2V2
V2 = 4.516 m/s
By bernoulli's equation,
P = 183023 Pa
Difference between the fluid pressure at location 2 and location 1 = 183023 Pa
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