Answer to Question #284678 in Physics for John

Question

A horizontal pipe 20.0 cm in diameter has a smooth reduction to a pipe 7.00 cm in diameter. If the pressure of the water in the larger pipe is 6.0 x 10 Pa and the pressure in the smaller pipe

s 3.0*10^ 4 Pa , at what rate does water flow through the pipes?

Answer 1

The speed of water is

$$v=\sqrt{2(p_2-p_1)/\rho},\\\space\\ v = \sqrt{2·(30000-60)/1000} = 7.7\text{ m/s }.$$

The volumetric flow rates:

$$Q_L=v·\pi R_L^2=0.24\text{ m}^2/\text s,\\\space\\ Q_S=v·\pi R_S^2=0.03\text{ m}^2/\text s.$$