The force (F) required to maintain the flow of layers of a liquid is equal to (A = area of contact of layers, dz = distance between the layers, du = change in velocity, \(\eta\) = coefficient of viscosity)
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Remember Newton's law of viscosity as "Stress is proportional to Strain Rate".
Stress = Force/Area.
Strain Rate = Velocity Gradient (\(du/dz\)).
The proportionality constant is the viscosity (\(\eta\)).
This gives \(F/A = \eta (du/dz)\), which is the fundamental equation for viscous force.