Fluids in motion (Bernoulli's equation)

[Lunar Guy]

1. The time required to fill a bucket with water from a certain garden hose is 30.0 s. If you cover part of the hose's nozzle with your thumb so that the speed of the water leaving the nozzle doubles, how long does it take to fill the bucket?



2. Homework Equations : None required. I hope. Just in case: A1v1 = A2v2



3. I believe that it would take the same amount of time to fill the bucket with water with your thumb on the nozzle than it would without your thumb on the nozzle... But I'm not sure...

 

[Lunar Guy]

Bump. Can anyone help me out?

 

[Moetasim]

Your intuition is correct! According to Bernoulli's equation, as the speed of a fluid increases, its pressure decreases. In this case, by covering part of the nozzle with your thumb, you are increasing the speed of the water. However, this also means that the pressure inside the hose decreases, which results in a decrease in the rate at which water flows out. Therefore, the time it takes to fill the bucket would remain the same. This is because the volume of water flowing out of the hose per second (flow rate) is the same in both cases, so the total volume of water in the bucket would also be the same.