1. A viscous liquid of density p and viscosity u in the reservoir is driven by a belt moving at a constant speed of Uo.

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1 A Viscous Liquid Of Density P And Viscosity U In The Reservoir Is Driven By A Belt Moving At A Constant Speed Of Uo 1 (91.57 KiB) Viewed 24 times

1. A viscous liquid of density p and viscosity u in the reservoir is driven by a belt moving at a constant speed of Uo. As soon as the liquid exits the slot of height ho, its height decreases or increases to hi downstream, depend- ing on the height H of the liquid in the reservoir. Note that the liquid height everywhere on the belt is very small compared with the belt length and the slot is of length l. air 10 H liquid h(x) hi ho belt Uo (a) Derive the equation of motion of the viscous liquid in the slot and state the boundary conditions. (b) Find u(y) and Q in the slot. (c) Express u(y) in a non-dimensional form with the Reynolds number Re = (ho/l)pho(gH/U/H. (d) Sketch the velocity profiles in the slot and after exiting the slot for the following cases: (i) bị > ho (ii) h1 = ho (iii) hi <ho