Question

1. Water is poured into a tank of height 1m, width 0.3m and length 0.3m at a rate of Qin=6x10-5m3/s. An orifice of diameter 6mm is installed at one side of the tank to discharge the water (Fig. Q4a). The discharge coefficient is 0.64.

a) When the water level h=0.2m, determine the outflow discharge rate Qout. Also, determine whether the water level is rising or falling, and the rate of change of the water level.

b) What is the maximum water level h that can be attained?

Qin Qout Orifice Fig. Q4a

Answer 1

Size of tank = 0.3 times 0.3 times 1 m Q_in = 6 times 10^-5 m^3/sec diameter of orifice d = 6 mm c_d = 0.64 h = 0.2 m d = 0.006 m Q_out = c_d A times squareroot 2gh A = pi/4 (0.006)^2 A = 2.82 times 10^-5 m^2 Q_out = 0.64 times 2.85 times 10^-5 times squareroot 2 times 9.81 times 0.2 Q_out = 3.5 times 10^-5 m^3/sec Q_net = Q_10 in - Q_out = 6 times 10^-5 - 3.5 times 10^-5 Q_net = 2.5 times 10^-5 m^3/sec Q_net = c_d A squareroot 2gh 2.5 times 10^-5 = 0.64 times 2.85 times 10^-5 times squareroot 2 times 9.81 times h h_1 = 0.2 m \r\n when the water level rising h_2 = h + h_1 = 0.2 + 0.1 = 0.3 M h_2 = 0.3 M Q_in = c_d A squareroot 2gh 6 times 10^-5 = 0.64 times (2.82 times 10^-5) squareroot 2 times 9.81 times h