A shower head has 20 circular openings, each with radius 1.0 mm. The shower head is connected to a pipe with radius 0.80 cm. If the speed of water in the pipe is 3.0 m/s, what is its speed as it exits the shower-head openings?
Solution 35E Step 1 of 4: In the given problem, the water flows with speed v = 3 m/s i1 the pipe of radius r1= 0.8 cmand area A , whe1 it comes out of the shower head with n=20 circular opening with each circular opening radius r = 1 mm and area of one such opening A 1 2 1 1 with speed v f2om the total area at the head of shower A = nA =220A . We can find the speed of water when it comes out of shower using continuity equation. Step 2 of 4: The mass of a moving fluid doesn’t change as it flows. This leads to an important quantitative relationship called the continuity equation. Now let us Consider a portion of a flow tube between two stationary cross sections with areas A in t1e pipe and A at the2 shower head.The fluid speeds at these sections are v an1 v resp2ctively. No fluid flows in or out across the sides of the tube because the fluid velocity is tangent to the wall at every point on the wall. The continuity equation of the liquid is given by, A v = A v 1 1 2 2 Solving forv 2 v = A1v1 …………….1 2 A2