Question

# A liquid of density 1270 kg/m31270 kg/m3 flows steadily through a pipe of varying diameter and...

A liquid of density 1270 kg/m31270 kg/m3 flows steadily through a pipe of varying diameter and height. At Location 1 along the pipe, the flow speed is 9.61 m/s9.61 m/s and the pipe diameter ?1d1 is 10.7 cm10.7 cm. At Location 2, the pipe diameter ?2d2 is 16.1 cm16.1 cm. At Location 1, the pipe is Δ?=8.31 mΔy=8.31 m higher than it is at Location 2. Ignoring viscosity, calculate the difference Δ?ΔPbetween the fluid pressure at Location 2 and the fluid pressure at Location 1.

Gravitational acceleration = g = 9.81 m/s2

Density of liquid = = 1270 kg/m3

Pressure at location 1 = P1

Speed of flow at location 1 = V1 = 9.61 m/s

Diameter of pipe at location 1 = d1 = 10.7 cm = 0.107 m

Area of pipe at location 1 = A1 = d12/4

Pressure at location 2 = P2

Speed of flow at location 2 = V2

Diameter of pipe at location 2 = d2 = 16.1 cm = 0.161 m

Area of pipe at location 2 = A2 = d22/4

At location 1 the pipe is 8.31m higher than at location 2.

y = 8.31 m

Pressure difference at location 2 and 1 = P = P2 - P1

By continuity equation,

A1V1 = A2V2

(d12/4)V1 = (d22/4)V2

d12V1 = d22V2

(0.107)2(9.61) = (0.161)2V2

V2 = 4.244 m/s

By applying Bernoulli's equation,

P = 150738.05 Pa

P = 1.507 x 105 Pa

The difference between the fluid pressure at location 2 and the fluid pressure at location 1 = 1.507 x 105 Pa