I was drinking from a water fountain when I began thinking about how the principles behind how they work were related to the fluid physics we just learned. I decided to think about how much pressure must be generated at the pump for the water to shoot out for us to drink.
First I calculated the speed of the water. I estimated the height that it reached after shooting out from the fountain to be roughly 10cm. So we can calculate the water's velocity using conservation of energy.
mgh=1/2mv^2 (mass of the water doesn't matter here as it cancels out)
Then I found the speed of the water when it is still inside the pump using the equation of continuity. Here, I estimated the pipe in the fountain to be 1cm in diameter and the diameter of the nozzle to be 0.3cm
Finally, I used Bernoulli's equation to find the pressure generated by the pump. I used the location right after the water exits the nozzle as one reference point and the water at the pump (estimated to be roughly 1 meter below the nozzle).