a) ( 50 p) A cylindrical water tank that is placed at the top of a bullding discharges through a steel pipe as shown in the figure. The tank is initially filled with water to an elevation of H with respect to the reference plane. The pipeline has an equivalent length (Leq) of 100m and diameter of 23cm and the outlet of the pipe is open to atmosphere. a) (5 p) Apply mechanical energy balance between planes 1 and 2 and show that the velocity is: V22=2gh+d4fLin b) (15 p) Write mass-balance and show that the change in the liquid height with time is: 4D2dtdh=Q2=V24d2dt=(dD)22g1(1+d4fLeq)hdh c) (15 p) Taking f=0.0039, H=1m, calculate the time needed for h to drop from 4m to 1.5m. d) (15p) Plot the varlations of V2 and has a function of time on the same plot. Use MATLAB to solve the equation and plot the graphs