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Diwali Assignment of calculus...:

Assigned By: Prof. Manish K. Gupta

Course: SC 107

DA-IICT,

Gandhinagar.

Made by:  PARVA PATEL

ID:  201601415

Drainage of water from water tank, TORRICELLI’S LAW....:

A significant topic related to DIFFERENTIAL equation which will enlighten your      knowledge in the field of fluids..

1. Introduction:

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.
Torricelli’s law is a very important theorem in fluid dynamics which relates the speed of fluid flowing out of a hole(opening) created at any verticle section of the wall of tank to the height of fluid above the opening.

 

Torricelli’s law states that the speed of efflux, v, of a fluid through a 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.

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

(0.5)mv^2, with the potential energy lost,  mgh , and solving for v. ”

2. Motivation:

While searching for some project for application of differential equation, I was looking for something which I like. At that moment I remembered of the fluids which was one of my favourite topics in the higher classes....

So, I decided to make my project on the topic of Torricelli's law.... 

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