All practical fluids are viscous and offer resistance to fluid flow. So that there is some losses in fluid flow between two section. Bernoulli’s equation was derives on the assumption that fluid is non-viscous i.e. frictionless, which is not applicable of practical fluid and hence Bernoulli’s equation is modified by considering losses.

(i)    Modified Bernoulli’s equation for real fluid.

P₁ / γ + V²₁ / 2g + Z₁ = P₂ / γ + V₂² / 2g + Z₂ + hL

where hL = loss of energy between point 1 and 2.

(ii)    Modified Bernoulli’s equation in K.E. correction factor 'α' considered

P₁/ γ + α₁ V²₁/2g + Z₁ = P₂ / γ + α₂ V₂²/2g + Z₂

(iii)    Modified B.E. if some energy is taken out from 1 to 2

P₁/ γ + V²₁/2g + Z1 = P₂ / γ + V₂² / 2g + Z₂ + energy taken out

(iv)    Modified B.E. if energy is added from 1 to 2.

P₁/ γ + V²₁/2g + Z1 + energy added = P₂ / γ  + V₂² / 2g + Z₂

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