Final answer:
Torricelli's theorem states that the speed of fluid exiting an orifice is the same as if it fell freely through a height h, with this speed calculated using the formula v = sqrt(2gh). This assumes negligible resistance and involves using Bernoulli's equation to account for energy conservation between potential and kinetic energy.
Step-by-step explanation:
The subject of this question is Torricelli's theorem, which relates to the behavior of fluids and how they exit an orifice or hole in a container. According to Torricelli's theorem, if resistance (such as friction) is negligible, the speed of a fluid as it emerges from an opening is the same as the speed it would have if it fell freely through a height h (the distance from the fluid surface to the opening).
Torricelli's theorem can be derived from Bernoulli's equation, which states that the total mechanical energy of the flowing fluid is conserved. For a fluid flowing from the surface to the point of exit at a lower level, the energy conservation applied through Bernoulli's equation would equate potential energy at the surface with the kinetic energy at the exit point, assuming atmospheric pressure is the same at both points and the potential energy difference is due to the height h.
The velocity or speed of the efflux can be calculated using the formula derived from Torricelli's theorem: v = sqrt(2gh), where g is the acceleration due to gravity and h is the height of the fluid column above the opening.