Bernauli Theorem

There are two identical small holes on the opposite sides of a tank, hence velocities of liquid flowing out of both the holes are

v%20_%7B1%7D%3D%5Csqrt%7B2%20g%20(%20h%20%2B%20x%20)%7D%20%5Ctext%20%7B%20and%20%7D%20v%20_%7B2%7D%3D%5Csqrt%7B2%20g%20x%20%7D

Now, Volume of the liquid discharged per second at a hole is

Av%20%2C%5Cleft(%20v%20%3D%20v%20_%7B1%7D%5Cright.

v%5Cleft._%7B2%7D%5Cright)

Mass of liquid discharged per second is

Av%5Crho

, Momentum of liquid discharged per second is

Av%20%5E%7B2%7D%20%5Crho

The force exerted at the upper hole is

Ap%20%5Cleft(%20v%20_%7B2%7D%5Cright)%5E%7B2%7D

and The force exerted at the lower hole is

Ap%20%5Cleft(%20v%20_%7B1%7D%5Cright)%5E%7B2%7D

The net force on the tank is

F%3DA%20%5Crho%5Cleft%5B%5Cleft(%20v%20_%7B1%7D%5Cright)%5E%7B2%7D-%5Cleft(%20v%20_%7B2%7D%5Cright)%5E%7B2%7D%5Cright%5D

F%3DA%20%5Crho%5B2%20g%20(%20h%20%2B%20x%20)-2%20gx%20%5D

F%3D2%20Apgh

%5CRightarrow%20F%20%5Cpropto%20h

Chapter Questions
1 MCQs