How Fast Does Water Leave the Hole?

What is the horizontal speed at which the water leaves the hole in units of ms^-1?

The horizontal speed at which the water leaves the hole is 4.09 ms^-1.

What is speed?

Speed is the rate of change of the position of an object in a given direction. It is expressed as the distance traveled per unit of time, typically measured in meters per second (m/s). It is also commonly represented by the symbol ‘v’. Speed is a scalar quantity, meaning it has only magnitude, not direction.

How is the horizontal speed calculated?

The kinetic energy per unit volume at the point of the hole is equal to the density of the water multiplied by one-half the square of the velocity of the water leaving the hole.

Since these two values are constant across a horizontal streamline, we can set up the following equation:

ρgh = ρ(v^2/2)

Solving for v, we get:

v = √(2gh)

Plugging in the values for the height of the water above the hole (h = 0.4 m) and the acceleration due to gravity (g = 9.81 ms^-2), we get:

v = √(2*9.81*0.4) = 4.09 ms^-1

Therefore, the horizontal speed at which the water leaves the hole is 4.09 ms^-1.