Answer to Question #284679 in Physics for John

Question

Ashower head has 10 circular openings, each with radius 2.0 mm. The shower head is connected to a pipe with radius 0.70 cm. if the speed of water in the pipe is 4.0 m/s, what is its

speed as it exits the shower-head openings?

Answer 1

The volumetric flow rate is the same:

$$Q=v_1A_1=v_2A_2,\\\space\\ v_2=\dfrac{v_1A_1}{A_2}=\dfrac{v_1r_1^2}{r_2^2}=\dfrac{4·0.0007^2}{10·0.02^2}=0.049\text{ m/s}.$$