If  is height of the orifice above the ground and  is height of the liquid column from the ground (height of liquid's surface), then the horizontal distance covered by the jet of liquid to reach the same level as the base of the liquid column can be easily derived. Since  be the vertical height traveled by a particle of jet stream, we have from the laws of falling body
where  is the time taken by the jet particle to fall from the orifice to the ground. If the horizontal efflux velocity is , then the horizontal distance traveled by the jet particle during the time duration  is
Since the water level is  above the orifice, the horizontal efflux velocity  as given by Torricelli's law. Thus, we have from the two equations
The location of the orifice that yields the maximum horizontal range is obtained by differentiating the above equation for  with respect to , and solving . Here we have
Solving  we obtain
and the maximum range