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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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