Consider a cylindrical tank with a diameter D of 1.0m and a height H of 1.5m as shown in the sketch below. Water (ρ = 1000 kg/m³ enters the tank at the bottom through a tube with diameter d of 5mm at a constant average velocity of 4m/s. Initially (time t = 0), the tank is half full as shown; water continues to enter until the tank begins to overflow at time full. Selecting the water inside the tank at any instant as the control volume of interest, write or develop a formal explicit expression of mass conservation for this control volume. Your result should be in the form of an ordinary differential equation. Solve your differential equation for full and determine a numerical value for it using the data given.

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Vavg = 4 m/s D=1.0 m d=5 mm H = 1.5 m H/2