HAVE A GREAT DAY! :) I/I: In the 17th century, Evangelista Torricelli, discovered the mathematics that describe the force by which fluids will squirt out of a hole in a container. As it turns out, the only factor that effects the velocity of the water squirting out of the hole is the height (h) of the water in the tank above the hole. The velocity (v) can be calculated according to the following formula v=√2gh where g is the acceleration due to gravity = 9.8 m/s2 Research Torricelli’s law and design an experiment to test it.

Q 1: Describe your materials and methods needed to test Torricelli’s law.

A 1:

Q 2: Describe the independent and dependent variables in your experiment.

A 2:

Step-by-step explanation:

Torricelli's law, also known as Torricelli's theorem, is a theorem in fluid dynamics relating the speed of fluid flowing out of an orifice to the height of fluid above the opening. The law states that the speed of efflux, v, of a fluid through a sharp-edged hole at the bottom of a tank filled to a depth h is the same as the speed that a body (in this case a drop of water) would acquire in falling freely from a height h, i.e. {\displaystyle v={\sqrt {2gh}}}, where g is the acceleration due to gravity (9.81 N/kg near the surface of the earth). This last expression comes from equating the kinetic energy gained,

{\displaystyle{\frac {1}{2}}mv^{2}}, with the potential energy lost, mgh , and solving for v. The law was discovered (though not in this form) by the Italian scientist Evangelista Torricelli, in 1643. It was later shown to be a particular case of Bernoulli's principle.

The speed of a portion of water flowing through an opening in a tank a given distance, h, below the water surface is the same as the speed that would be attained by a drop of water falling freely under the force of gravity alone (that is, neglecting effects of air) through the same distance, h. The speed of efflux is independent of the direction of flow; at the point of the opening the speed is given by this equation, whether the opening is directed upward, downward, or horizontally.

DERIVATION

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Under the assumptions of an incompressible fluid with negligible viscosity, Bernoulli's principle states that:

where v is fluid speed, g is the gravitational acceleration (9.81 m/s2), h is the fluid's height above a reference point, p is pressure, and ρ is density. Define the opening to be at h=0. At the top of the tank, p is equal to the atmospheric pressure. v can be considered 0 because the fluid surface drops in height extremely slowly compared to the speed at which fluid exits the tank. At the opening, h=0 and p is again atmospheric pressure. Eliminating the constant and solving gives:

EXPERIMENTAL  EVIDENCE

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Torricelli's law can be demonstrated in the spouting can experiment, which is designed to show that in a liquid with an open surface, pressure increases with depth. It consists of a tube with three separate holes and an open surface. The three holes are blocked, then the tube is filled with water. When it is full, the holes are unblocked. The lower a jet is on the tube, the more powerful it is. The fluid's exit velocity is greater further down the tube.

Ignoring viscosity and other losses, if the nozzles point vertically upward then each jet will reach the height of the surface of the liquid in the container.

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step-by-step explanation: