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 (102.44 KiB) Viewed 45 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 9 H liquid 2 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) h1 > ho (ii) h1 = ho (iii) h1 < ho