It is a home work question, full question below: In a water tank, shaped like a cylinder, water flows into the top of the tank at an inflow rate (liter / min) given at v1 (t). At the same time, the water flows out through a hole in the bottom, with an outflow rate given at v2 (t). V (t) indicates the volume of water in the tank at one arbitrary time, t. (a) Make a figure and find a general expression for V (t), expressed by V (0), v1 (t) and v2 (t). We assume that the inflow rate into the tank v1 (t) is constant equal to 5 liters / min, while the outflow rate is given at v2 (t) = 1/( t + 1) . (b) How much water is there in the tank after 19 minutes?
In task a I have V(t)=V(0)+v1(t)-v2(t) as the general expression, I am not sure if its correct In task b i have tried to integrate 1/t+1 from 0 to 19 and got 3 and v1=95 liters after 19 minutes, as the differnce is so big i think I did something wrong. I also assume V(0)=full tank as v2 gets smaller and smaller as time passes. So from my calculations the tank contains 92 liters after 19 minutes, is this correct?