Plate Oil film Air
Oil, of density ρ and viscosity μ , drains steadily down the
side of a vertical plate, as in Fig. P4.80. After a development
region near the top of the plate, the oil fi lm will
become independent of z and of constant thickness δ .
Assume that w = w ( x ) only and that the atmosphere offers
no shear resistance to the surface of the fi lm. ( a ) Solve the
Navier-Stokes equation for w ( x ), and sketch its approximate
shape. ( b ) Suppose that fi lm thickness δ and the slope
of the velocity profi le at the wall [ ∂ w /∂ x ] wall are measured
with a laser-Doppler anemometer (Chap. 6). Find an
expression for oil viscosity μ as a function of ( ρ , δ , g ,
[ ∂ w / ∂ x ] wall ).
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