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Consider fluid flow between two infinite horizontal plates which are parallel (the gap between them being 50 mm). The top plate is sliding parallel to the stationary bottom plate at a speed of 3 m/s. The flow between the plates is solely due to the motion of the top plate. The force per unit area (magnitude) required to maintain the bottom plate stationary is __________ N/m2.

Viscosity of the fluid μ = 0.44 kg/m-s and density ρ = 888 kg/m3.

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According to Newton’s law of viscosity.

\(\tau = \mu \frac{{du}}{{dy}}\)

& as the profile is assumed to be linear, then

\(\tau = \mu \frac{v}{y}\)

Here, y = 50 mm = 0.05 m, v = 3 m/s, μ = 0.44 kg/ms

\(\tau = \frac{{0.44 \times 3}}{{0.05}} = 26.4\;N/{m^2}\)

Key point

Force per unit area is the stress applied here.

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