Question

Homework 9 Water towers store water so pumps may run only when needed, rather than continuously. The figure shows a diagram of a water tower. Water has a density of Pw 1. A worker periodically tests the water at the test point at the base of the tower. What is the pressure of the water at this point? (gauge pressure) Figure 1: A cross section of a water tower is shown 2. The worker leaves the valve open for a while to clear The testing line leads from near surface of the w out the water that has been sitting in the pipe leading to the ter in the tower to valve at the base. The length testing point. If the output has a diameter of a, what is the of the testing line is h. speed of the stream of water at this point? 3. How long does it take to completely clear the line of old water?

Answer 1

somt 1) The pressure of the water at the base of the tower is the gauge pressure. Thus, the pressure at the bottom is: - P bottom = Patm t sew gh latm 22 Here, Patm Atmospheric pressure. hay sw density of water h water level from the base of tower g acceleration due to gravity Now, consider the case when there are holes both at the top and bottom of the testing point). Thus, the pressure at the top and bottom are both equal to atmospheric pressure Also, the velocity at the top is very less than the velocity of water at the bottom hole of the tower Thus, & e [Here, &, velocity of water at top V₂> velocity at from Bernoulli's equation: - bottom P + 2 + 2 = P₂ + B + 2 igig" sg eg Bg 28th ~2 +2, + z2 29 Now, , << V₂, so take v no .. = 2, - Z & J2g(2,-2) (As n = 2, -22) a = √2gh low, &, sav

Here, a area consider volume of the tank as v. Then, time required to empty the tank is, &- v a legh I volume of water in tank - volume empty by] trole in time et - V - array length/distance - - a x stime x velocity - v - ax tx .2gh. + = arran