Question

A rectangular water tank is divided by a partition into two chambers, as shown in Fig. 17-23a. In the bottom of the partition is a round, sharp-edged orifice with a diameter of 150 mm. The coefficient of discharge for the 4. is 0.62. At a certain instant, the water level in chamber B is 2.5 m higher than it is in chamber A. How long will it take for the water surfaces in the two chambers to be at the same level? 2.5m Water Onifice 2.0 m 3.0m

Answer 1

Change in valume dv = CA squareroot 2gh dt h rightarrow difference in elivation of two water levels at any time dh rightarrow change in h in time dt dv rightarrow volume of water moving in changes A in time dt volume of water leaving B is equal to volume entering A 2 times 7.5 (dh_B) = 2 times 3(dh_A) dh_A = 2.5 dh_B........(1) also dh = dh_B + dh_A...(2) from 1 and 2 dh = dh_B + 2.5 dh_B dh = 3.5 dh_B \r\n dh_B = dh/3.5 dv = dh/3.5 times 2 times 7.5 = 15 dh/3.5 area A = pi/4 times .15^2 = 0.17671 mm^2 15/3.5 dh = 0.62 times 0.17761 squareroot 2 times 9.81 times h^1/2 dt = 8.83 dh = h^1/2 dt integral^t_0 dt = 8.83 integral^2.5_0 h^1/2 dh [t]^t_0 = 8.83[2h^1/2]^2.5_0 t = 27.92 sec