Mechanical Properties of fluids [Bernoulli Principle]

Chapter-2  Mechanical Properties of Fluids

Bernoulli Principle-

Bernoulli Principle-It states that the sum of pressure energy, Kinetic energy, Potential energy per unit volume of an incompressible, no viscus fluid in a streamlined in rotational  flow remains constant along a streamline.

Mathematically-

P+ 1/2ρv²+ ρgh =constant 

Derivation-

Consider a non-viscus incompressible fluid flow steadily between section A and B of a pipe of varying cross-section A and B show in figure.

Let A₁, A₂ be the cross-section areas at point A and B respectively. V₁ and V₂ be velocity at cross-section A and B. H₁ and H₂ be the height of  point and be at and A and B respectively. let ρ be the density of the fluid. m is the mass of the fluid enter in the pipe at section point A in time Δt must be flow out at section B at time  Δt.

mass=volume * density
mass=area *distance* density

m=a₁v₁Δtρ
And it also equal to the mass flow out of pipe in Δt time. then

m=a₁v₁Δtρ=a₂v₂Δtρ
      a₁v₁=a₂v₂              { i.e. equation of continuity }

Change in Kinetic Energy(K.E.)-
K.E. at B - K.E. at B
  1/2mv²₂ - 1/2mv²₁
  1/2m(v²₂ - v²₁)

Change in Potential Energy(P.E.)