Question

Explain and proof the Bernoulli Principle don't copy and answer asap

Answer 1

Heya!
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★Bernoulli's Principle ★
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=> This principle states that for the stream line flow of an ideal liquid , the total energy per unit mass remains constant . 


[ Note : I am using ¶ for density ] 


→ Expression : 
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=> P/¶ + ½v² + gh = constant . 


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★Proof : We know that an ideal liquid has three kinds of energies . So now we shall calculate all energies divided by the unit mass. 


1. ) pressure energy = pressure × volume 

=> P × ¶ / M [ as density = Mass / Volume ] 

=> Energy per unit mass = P × ¶ / M × 1 /M


= P / ¶ -------------- ( 1. )



2. ) Kinetic Energy = ½ mv²


=> Energy per unit mass = ½ mv² × 1 / m 


=> ½ v²-------------( 2. )



3. ) Potential Energy = mgh 


=> Energy by unit mass = mgh/m 


=> gh-------------(3.)



★Now , from the work energy principle, we know that work done is equal to the change in kinetic energy . I,e 


dW = Kf - Ki 


Thus , we have 


(P1/¶- P2 /¶ ) = ( ½v2² - ½v1²) - ( gh1 - gh2)


=> Thus, this expression can be written as - 


•°• P1/¶ + ½v1² + gh1 = P2/¶ + ½ v2² + gh2 



Thus , it is proved that the total energy has remained as a Constant !! This is what is stated by the principle . 


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Answer 2

Explanation:

Bernoulli's principle formulated by Daniel Bernoulli states that as the speed of a moving fluid increases (liquid or gas), the pressure within the fluid decreases. Although Bernoulli deduced the law, it was Leonhard Euler who derived Bernoulli's equation in its usual form in the year 1752.