Question

Daniel's good friend Giovanni Venturi joined him for another round of fraps. They were discussing ways to determine the velocity of water in a pipe. If the pressure drops 650 kPa as water flowing in a 31 cm diameter pipe is forced to flow through a 19 cm diameter portion, what is the velocity of the water in the 31 cm section of pipe?

Answer 1

Step-by-step explanation:

Given

Pressure drop
`\Delta P=650\ kPa`

inlet diameter
`d_1=31\ cm`

Outlet diameter
`d_2=19\ cm`

density of water
`\rho=10^3\ kg/m^3`

Suppose
`v_1` and
`v_2` be the inlet and outlet velocity

According to continuity equation

`A_1v_1=A_2v_2`

where A=cross-section of Pipe

`A=(\pi d^2)/(4)`

thus
`d_1^2v_1=d_2^2v_2`

`v_2=v_1* ((d_1)/(d_2))^2`

`v_2=v_1* ((31)/(19))^2`

Also from Bernoulli's Equation

`\Delta P=(1)/(2)\rho (v_2^2-v_1^2)`

`650* 10^3=(1)/(2)* 10^3* (v_1^2((31)/(19))^4-v_1^2)`

`v_1=√(106.79)`

`v_1=10.33\ m/s`