Answer to Question #92770 in Mechanics | Relativity for Vaibhavi Desai

Question

1. An ideal fluid flows at 15.5ms^-1 in a horizontal pipe down the line, the pipe diameter changes to 1/3 of its original diameter what is the flow speed of the fluid in this section if the original diameter of the pipe was 6m?

Answer 1

Continuity equation states

$$A_1v_1=A_2v_2$$

So

$$v_2=\frac{A_1}{A_2}v_1=\frac{\pi d_1^2/4}{\pi d_2^2/4}v_1=\frac{d_1^2}{d_2^2}v_1=\frac{d_1^2}{d_1^2/9}v_1=9v_1$$

$$=9\times 15.5\:\rm{m/s}=139.5\:\rm{m/s}$$