An open, vertical, cylindrical water storage tank of radius 1.5 m (s2xglgt2idcjvwsvwpc+goky3uamohfohe qzbvue) and height 10 m (amxelftksuqmcc) that is initially empty is being filled from above at a rate of 2 m3/min3vv3jxf+av3l3pfp1nupelftksuqm cc. there is an open outlet pipe of radius 0.28 m (d47l29eomeioqsdzdful0avpkh4agrgtdd uzil7v) at a height of 2 m (rte0du31s2sgzwsuvork5cyii=) above the bottom of the tank. intuitively, the velocity (and therefore flow rate) of water through this outlet pipe depends on the height of the column of water above the outlet. hint: you may assume the flow of the water outlet is frictionless, the pressure is 1 atm at all points outside the tank, and that the velocity of the top water/air interface is zero.
part a) taking time = 0 minutes to be the instant that water begins flowing into the tank, how long will it take (in minutes) for the outlet flow of water to begin?
part b) after the outlet flow begins, derive a differential equation that expresses the change in height of the water in the tank over time in terms of the parameters given in the problem statement. keep this equation in algebraic form; do not plug in the numerical values of the parameters yet
part c) calculate the steady-state height of water in the tank (measured from the bottom)
part d) using euler’s method, plot h(t), starting at 0 min and ending when the steady-state value is 99.9% achieved.