Final answer:
Torricelli's law connects the speed of a fluid exiting an opening to the height of the fluid above the opening, based on Bernoulli's equation demonstrating the conservation of energy in a fluid system. Fluid pressure decreases as speed increases, and this effect is used in devices such as pitot tubes to measure fluid speeds.
Step-by-step explanation:
Torricelli's law is a theorem in fluid dynamics relating the speed of fluid flowing out of an opening to the height of the fluid above the opening. According to this law, if resistance is negligible, the speed at which fluid leaves an opening is equivalent to the speed it would have if it fell from a height h above the opening, which is the height of the fluid surface above the exit point. This principle stems from Bernoulli's equation, which expresses the conservation of energy for an incompressible fluid in the absence of friction.
Bernoulli's principle also indicates that when a fluid flows at a constant depth, pressure decreases as speed increases. This can be observed when comparing the flow speed and pressure at two different points along a fluid's path. Additionally, the mass flow rate, representing the mass of fluid passing through a point per unit of time, maintains a constant relationship between velocity and cross-sectional area, based on the principle of conservation of mass.
The practical applications of Bernoulli's principle and Torricelli's law can be seen in instruments like the Prandtl tube, also known as a pitot tube, which measures fluid speed by taking advantage of the relationship between pressure and velocity.