A liquid flows down an inclined plane surface in a steady, fully developed laminar flow of thickness h. a) Simplify the continuity equations and Navier-Stokes equations to model this flow field. Clearly state all assumptions. b) Obtain expressions for the liquid velocity profile, the volume flow rate and the average velocity. c) Relate the liquid thickness to the volume flow rate per unit depth of surface normal to the flow. d) Calculate the volume flow rate in a film water h = 1 mm thick, flowing on a surface b = 1 m wide, inclined at e = 15° to the horizontal. (Awater = 1000 kg/m, µ water 1.0 x 10° kg/ms, g = 9.81 m/s³) h =1 mm 8 = 15° Width of surface = 1 m Figure 03

Elements Of Electromagnetics
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A liquid flows down an inclined plane surface in a steady, fully developed laminar flow of
thickness h.
a)
Simplify the continuity equations and Navier-Stokes equations to model this flow field.
Clearly state all assumptions.
b)
Obtain expressions for the liquid velocity profile, the volume flow rate and the average
velocity.
c)
Relate the liquid thickness to the volume flow rate per unit depth of surface normal to
the flow.
d)
Calculate the volume flow rate in a film water h = 1 mm thick, flowing on a surface
b = 1 m wide, inclined at 0 = 15° to the horizontal.
(Pwater = 1000 kg/m³ , µ water 1.0 x 10° kg/ms, g = 9.81 m/s)
h =1 mm
8 = 15°
Width of surface = 1 m
Figure Q3
Transcribed Image Text:A liquid flows down an inclined plane surface in a steady, fully developed laminar flow of thickness h. a) Simplify the continuity equations and Navier-Stokes equations to model this flow field. Clearly state all assumptions. b) Obtain expressions for the liquid velocity profile, the volume flow rate and the average velocity. c) Relate the liquid thickness to the volume flow rate per unit depth of surface normal to the flow. d) Calculate the volume flow rate in a film water h = 1 mm thick, flowing on a surface b = 1 m wide, inclined at 0 = 15° to the horizontal. (Pwater = 1000 kg/m³ , µ water 1.0 x 10° kg/ms, g = 9.81 m/s) h =1 mm 8 = 15° Width of surface = 1 m Figure Q3
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