state and prove bernuolli principal for the flow of non viscous
Answers
Answer:
Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. Derivation : Let the velocity, pressure and area of a fluid column at a point A be v₁, p and A₂ and at another point B be v₂, p₂, p₂ and A₂ .
Hi there , its very simple. lemme break it down for you.
Bernoulli's principle states that the sum of the pressure energy , potential energy and kinetic energy remains constant in an incompressible fluid.
consider a pipe of area of cross section a1 and a2. liquid of density rho ρ enters with velocity v1 and leaves with velocity v2. it is at a height of h1 and h2 from the ground. part A is where liquid enters , part B is where liquid leaves .
partA: Pressure energy: P1 kinetic energy: 1/2mv1² potential energy: ρgh1
Part B: pressure energy=p1 kinetic energy=1/2mv2² potential energy=ρgh2
work done=gain in PE+KE
p1+p2=1/2m(v2-v1)² + ρg(h2-h1)
=p1+p2=1/2mv2²-1/2mv1² + pgh2²-pgh1²
bringing all the terms containing 1 to one side and terms containing 2 to the other side , we get :
p1+1/2mv1²+ρgh1=p2+1/2mv2²+ρgh2
this is the proof.