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Torricelli's Law

Last updated date: 23rd May 2024
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What is Torricelli's Law?

The law of Torricelli is also called Torricelli's theorem. This is a theorem in fluid dynamics which is simply relating the speed of fluid that is flowing from an orifice to the height of fluid above the opening. 

The law states that the speed denoted as v that is of efflux 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 that is in this case a drop of water would acquire in freely falling from a height that is h which is written as: 

V = \[\sqrt{2gh}\]

where the letter g is the acceleration which is due to gravity that is 9.81 m/s2 near the Earth surface. 

On this page, we are going to learn more about the law.

Torricelli's Theorem

The theorem of Torricelli is also known as Torricelli’s principle or the equation of Torricelli equation. That statement is the speed v of a liquid that is flowing under the force of gravity out of an opening in a tank is proportional jointly to the square root of the vertical distance. The distance denoted by h which is between the liquid surface and the centre of the opening and to the square root of twice the acceleration caused by gravity that is 2g or simply v =  2gh1/2

(The value which is of the acceleration caused by gravity at the surface of Earth is about 32.2 feet per second per second or 9.8 metres per second per second. The theorem is said to be named after Evangelista Torricelli who discovered it in 1643).

The speed of water which is flowing through an opening in a tank at a given distance denoted by ‘h’ is the same as the speed that would be attained by a drop of water falling freely under the force of gravity alone.' This is considered neglecting effects of air which is through the same distance as h. 

The speed of efflux is said to be independent of the flow of the direction. At the point of the opening, the speed is given by this equation irrespective of whether the opening is directed upward or downward or even horizontally.

Torricelli Experiment

In the early 1600s, Sir Galileo argued that a pump of suction was able to draw water from a well because of the "force of vacuum" which is inside the pump. Then after Galileo's death, there was an Italian Mathematician and Physicist Evangelista Torricelli 1608-1647 who proposed another explanation. He suggested that the air which is in our atmosphere has weight and that the force that is of the atmosphere pushing down on the surface of the water usually drives the water into the suction pump when it is evacuated.

In the experiment conducted, some but not all of the mercury was drained out of the glass tube and it slipped into the dish. The explanation of Torricelli was that by assuming that mercury drains from the glass tube until the force of the column of mercury pushing down on the inside of the tube exactly balances the force of the atmosphere which is pushing down on the liquid surface from outside of the tube.

Torricelli predicted that the height of the column of mercury would generally change from day to day as the pressure of the atmosphere changed. Today his apparatus is called a barometer derived from the Greek “baros” that means "weight," because it literally measures the weight of the atmosphere. Thus, we can say that a standard unit of pressure called the atmosphere pressure was defined as follows.

1 atm = 760 mmHg

1 torr = 1 mmHg

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On a sunny day, at sea level, there is the weight of a 760-mm column of mercury which is inside a glass tube that generally balances the weight of the atmosphere that is generally pushing down on the pool of mercury that surrounds the tube as well.  Therefore, we can say that the pressure of the atmosphere is said to be equivalent to 760 mm Hg.


Torricelli Equation

In terms of Physics, the equation of Torricelli's or the formula of Torricelli's is an equation created by Evangelista Torricelli. The equation itself is:

Vfx2 = Vix2 + 2axΔx

The term Vfx is the object's velocity that is final along the x-axis on which the acceleration is constant.

The term Vix is the object's velocity which is the initial along the x-axis.

The term ax is the object's acceleration which is along the x-axis, given as a constant.

The term Δx is the change of the object's position along the x-axis, also known as displacement.

This equation is said to be valid along any axis on which the acceleration is constant.

FAQs on Torricelli's Law

Q1. Explain Torricelli's Law of Efflux.

Ans: According to the law, that the speed of efflux of a fluid denoted by ‘v’ through a sharp-edged hole that is at the bottom of a tank which is filled to a depth denoted by the letter ‘h’ is the same as the speed of a body. This is the speed a drop of water would generally acquire in falling freely from a height denoted h.

Q2. Explain What Torricelli's Law Describes.

Ans: The theorem of Torricelli's is also known as Torricelli's law, The principle of Torricelli's or we can say that equation of Torricelli's states that speed that is denoted as v of a liquid flowing under the gravity's force out of an opening in a tank is proportional jointly to the square root of the vertical distance that is denoted as h between the liquid surface and the centre.

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