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

Answer:

$8.16\ \text{m/s}$

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 = $\pi\dfrac{d^2}{4}$

From the continuity equation we get

$A_1v_1=A_2v_2\\\Rightarrow \pi\dfrac{d_1^2}{4}v_1=\pi\dfrac{d_2^2}{4}v_2\\\Rightarrow v_2=\dfrac{d_1^2}{d_2^2}v_1\\\Rightarrow v_2=\dfrac{4^2}{1.4^2}\times 1\\\Rightarrow v_2=8.16\ \text{m/s}$

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