Question 6 A liquid flows down an inclined plane surface in a steady, fully developed laminar film of thickness h. Simplify the continuity and Navier-Stokes equations to model this flow field. Obtain expressions for the liquid velocity profile, the shear stress distribution, the volume flow rate, and the average velocity. Relate the liquid film thickness to the volume flow rate per unit depth of surface normal to the flow. Calculate the volume flow rate in a film of water h = 1 mm thick, flowing on a surface b = 1 mm wide, inclined at 0 = 15° to the horizontal. 0 15° h = 1 mm Width b = 1 m Answer: upg Q = V sine μ Txy = pgsine (h - y) bpgsine h³ μl 3 = Q bh v-22²) = hy bpgsinፀ h3 μ 3 h = 3μQ bpgsine Q = 0.846 L/s 1/3

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Properties of Fluids

The term fluid represents a type of substance that can easily change its shape under any external pressure/force and can flow. Fluids can acquire any shape in which it is stored and can resist normal stresses but cannot resist shear stress in rest condition. Whenever external shear stress is applied to fluids, it starts to flow. The fluids may be liquid or gas. Example- water, air, etc.