A cylindrical tank of diameter D is filled to a depth as illustrated in Figure 3.12. At a plug is pulled from the bottom of the tank and the volumetric flow rate through the orifice is given by what is sometimes known as Torricelli's law Q= C_d*A_o*sqrt(2*deltap/p) Here C_d is a discharge coefficient having a value of 0.6 and A_o is the area of the orifice. If the cross-sectional area of the tank is large compared to the area of the orifice, the pressure in the tank is essentially hydrostatic and delta p is given by Deltap = rou*g*h where h is the depth of the fluid in the tank. This leads to Torricelli's law in the form Q= C_d*A_o*sqrt(2gh), hydrostatic conditions
Use this information to derive an equation for the depth of the fluid as a function of time. For a tank filled with water to a depth of 1.6 m having a diameter of 20 cm, how long will it take to lower the depth to 1 cm if the diameter of the orifice is 3mm?