bernoulisequation

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