Bernoulis equation:

It denotes the interconversion of energies

Forces that at includes

Rate of work done by pressure from surroundings

Rate of energy obtained from internal energy reversible conversion

Rate of energy obtained due to reversible conversion of energy

Rate of work done by mechanical forces

Consider a pipe with an inlet and out let

With pressure p1, area a1, velocity of fluid be v1 at inlet

P2, a2,v2 be at the outlet

P1,a1,v1 -------------------- p2,a2,v2,

--------------------

Total energy = kinetic energy+ potential enrgy

TE1 = KE1+PE1

TE1 = ½ mv1*v1 +mgz1

,m (v1*v1/2 +gz1)

TE2 = ½ mv2*v2 +mgz2

,m(v2*v2/2 +gz2)

W = ,m(v1*v1/2 +gz1)-,m(v2*v2/2 +gz2)

,m [(v2*v2/2- v12/2)+g(z2-z1)]

W = W2-W2

(P2*m/ſ)+(P1*m/ ſ)

,m(p2-p1)/ ſ

m(p2-p1)/ ſ = m [(v2*v2/2- v1*v1/2)+g(z2-z1)]

(p2-p1)/ ſ = [(v2*v2/2- v12/2)+g(z2-z1)]

(p2-p1)/ ſ - [(v2*v2/2- v12/2)+g(z2-z1)] = constant

Correction factors

1) kinetic correction factor = ά

To eliminate the problem of integration it must be introduced

(p2-p1)/ ſ - [ά (v2*v2/2- v1*v1/2)+g(z2-z1)] = constant

2)Pump work correction factor

ή= wp – Hfs / wp

wp – Hfs = ήwp

ήwp +(p2-p1)/ ſ - [ά (v2*v2/2- v1*v1/2)+g(z2-z1)] = constant

3)Friction correction factor:

ήwp +(p2-p1)/ ſ - [ά (v2*v2/2- v1*v1/2)+g(z2-z1)]+ hf = constant

limitations of bernoulis equation

1) applicable only for ideal fluids

2) Total heat cannot be transferd from one point to another completely

keywords: bernoulis equation , limitations of bernoulis equation, correction factors in bernoulis equation

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