ooo Verizon 737 PM 35 Consider the conical tank which drains

..ooo Verizon 7:37 PM 35% Consider the conical tank which drains thr 1 Toericell\'s law states that when the surface of the water is at height h, the water draiss with a velocity it would have if it fell freely from beight h. Find the terminal velocity of an object that falls from bright Alo)-h, wwing the stasdard gravity differveanial equstion V294 2. The rate the water is lowing out is flowing out of the tank is the area of the hole times the velocity of of the draining wiater. Write the differential equation for the change of the water ip the tank dle de 3. The volume of the tank at time t is given by the cross-sectional area times the beight, v(t)-Tr2h(t). Differentiate this with respect to time to fad another dieetial equation for the change in volume of the water in the tank Tr..) d 6

Solution

Answer: Yes, we would be able to tell how full the tank was when we started draining it. This can be done by first

     integrating the expression for the dv/dt, that we have got in #3 this would give us the expression for the

     volume of the tank V(t) at any time t, and then we plug the value of t* and equate the expression V(t*) to

     0 and solve for the constant of integration C level of the tank.

     The value of C is the nothing but the volume of the tank initially (i.e. the C will tell us about how full the

     tank was when we started to drain the tank.)