Imagine a cylinder with a cross sectional area (a=1m). this container is filled with water to a height of 30m (h0=30m). if said cylinder is left open to the atmosphere so the water evaporates and the height decreases with time. in this problem, we will assume that the evaporation rate is independent of h.

part 1) why is our assumption unrealistic? i believe this is because we are assuming that height has no effect on our vapor pressure and in turn our rate of evaporation. this is opposed to the reality of the situation, as when there is less water, the rate of evaporation will decrease as there is less vapor pressure from our fluid in the container on the atmosphere our fluid is exposed to.

part 2) regardless, perform calculations with this assumption in place. if lw =(rate of evaporation/unit areasurface)=6-2 (molwater/m2s), construct an ordinary differential equation to relate h and lw.

part 3) show that height decreases linearly with time by integrating our constructed differential equation and calculate when the container will be empty.