Funnel or Cone, Which one empties first?

 

Which Tank empties first?

On first look it may appear that both are of same quantity, so both will take the same time to empty. 

However as we see closely, we see that tank 1 has more water on the top and less water in the bottom. We keep the water tanks at the highest floor, so that the water flow will be higher. So intuitively we can say that tank 1 has the advantage of emptying first. In the tank 2 when the water level has dropped, pressure at the orifice will drop, but it has got more quantity of water to empty, which will take more time.

(Principles involved: Higher the liquid column, higher the pressure at the orifice in the bottom, so higher velocity of exit flow by Toricelli's exit flow method, so higher the quantity of water flowing out.)

Found this interesting youtube video showing an experimental trial.

This is a good example of how we can make use of Calculus for real life problems where the quantities are changing continuously w.r.t to another quantity. Here the rate of water flowing out of the tank depends on the height of the water column, which is not constant and is changing w.r.t time as the water flows out. 

For Truncated cone:

For Truncated Funnel (Inverted Cone): Volume of Truncated cone derived.

Coefficient of Discharge Cd is an efficiency multiplier in fluid mechanics problems involving flow of liquid through orifices. Cd = Actual Flow / Theoretical Flow (Area x Velocity). This is necessary to bridge the gap between the theory and practice. can be seen as a calibration constant  

For Cone: