Question

A liquid of density 1190 kg/m3 flows steadily through a pipe of varying diameter and height. At Location 1 along the pipe, the flow speed is 9.63 m/s and the pipe diameter d1 is 12.7 cm. At Location 2, the pipe diameter d2 is 16.3 cm. At Location 1, the pipe is Δy=9.27 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.

Answer 1

143kW

Step-by-step explanation:

Given:

`v_1`=9.63m/s

Δy=
`z_2-z_1`=9.27 m

density'ρ'=1190 kg/m3

According to Bernouilli :

p/ρ + gz + (1/2)v² = constant.

Also vA = constant, so vr² = constant.

Hence, at location 2, the speed is (9.63 m/s)(12.7²/16.3²),

that is,
`v_2` = 5.85 m/s.

`p_2-p_1` = ρ { g(
`z_1-z_2`) + (
`(1)/(2)`)[
`v_1^2-v_2^2`] }

= (1190 kg/m³) [9.8 m/s² (9.27 m) + (
`(1)/(2)`)(9.63² - 5.85 ²)m²/s²]

`p_2-p_1` =143kW