Consider a fluid element of radius ‘r’, sliding in a cylindrical fluid element of radius (r + dr).

Let length of fluid element = dx.

Let ‘p’ be the pressure acting on face AB and ( P+ ∂p / ∂x dx ) be the pressure acting on face CD.

Let shear force on the surface of fluid element is τ x (2 πr dx)

Net force = ma         fluid flow with very low velocity, a = 0

Pπr² - ( p + ∂p / ∂x dx ) πr² - τ (2 πr dx)  =  0

Pπr² - Pπr² - ∂p / ∂x dx πr² - τ (2πrdx)

∂p / ∂x dx πr² = - τ (2πrdx)

∂p / ∂x = - 2τ / r

τ  = -r ∂ p / 2 ∂x

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