Horizontal range

Derivation

Applying Bernoulli's theorem,

Total energy per unit volume at the orifice = Total energy per unit volume at free surface

Which is the equation for the velocity of efflux.

Let a body fall freely from the level of free surface of the liquid. Let V be the velocity acquired by the body when it reaches the level of orifice

Now, 'u' = 0, 'v' = V, 'a' = g, 'S' = h

From equation (1) and (2), v = V

So, the velocity of efflux of a liquid is equal to the velocity acquired by the body in falling freely from the free surface of the liquid to the orifice.

This proves Torricelli's theorem.

Horizontal range: The escaping liquid flows in the form of a parabola. Let t be the time take by the liquid to fall through a height h'.

Let R be the horizontal range. In order to calculate R, we shall consider the horizontal motion of the projectile. The horizontal motion and taked place with constant velocity v.

For a given height of the liquid column, this range is maximum when h = h'.

If the liquid jet is directed upward, it should rise to the level of free surface of the liquid. But due to viscosity and air resistance , the actual height is always less.