Question

A water pipe having a 4.00 cm inside diameter carries water into the basement of a house at a speed of 1.00 m/s and a pressure of 167 kPa. The pipe tapers to 1.4 cm and rises to the second floor 7.8 m above the input point. What is the speed at the second floor

Answer 1

`8.16\ \text{m/s}`

Step-by-step explanation:

`d_1` = Initial diameter = 4 cm

`v_1` = Initial velocity = 1 m/s

`d_2` = Final diameter = 7.8 m

`v_2` = Final velocity

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

From the continuity equation we get

`A_1v_1=A_2v_2\\\Rightarrow \pi(d_1^2)/(4)v_1=\pi(d_2^2)/(4)v_2\\\Rightarrow v_2=(d_1^2)/(d_2^2)v_1\\\Rightarrow v_2=(4^2)/(1.4^2)* 1\\\Rightarrow v_2=8.16\ \text{m/s}`

The speed of water at the second floor is
`8.16\ \text{m/s}`.