Net force in the direction of flow  = 0

p₁A – p₂A = Force due to shear
                   = Shear stress x Surface area

(p₁ – p₂)A = τ₀ x π dL

(p₁ – p₂) π / 4 d² = τ₀ π dL

p₁ – p₂ = 4τ₀ L / d

by we know that,

hf = p1- p2 / ρg = 4 Flv2 / 2 gd

p₁-p₂ = 4fL V² / 2gd x ρg

p₁ – p₂ = 4fL V^₂ / 2gd x ρg

p₁ – p₂ = 4fL V²ρ / 2 d

Equating Equation (i) and (ii) we get,

4fLV²ρ / 2d  = 4 fLV²ρ / d

f = 2τ₀ / ρV²

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