A 20(deg) roof with respect to the horizontal is to be covered with a 0.25 in. layer of liquid roofing asphalt. Find the minimum effective kinematic viscosity of the asphalt in a 6 hr. period if the top surface of the layer is not to move more than 0.00100 in. relative to the bottom surface, and the width of the covered surface is 30 ft.
Work:
Fluid is viscous and incompressible
change in time = 6 hours
asphalt layer = 0.25 inch
change in x of asphalt layer = 0.00100 inch
width of covered surface = 30 ft
v = kinematic viscosity = absolute viscosity mu/density ro
VU = velocity of upper plate = Ui + Vj
VL = velocity of lower plate = U'i + V'j
VT = total velocity = U(z)i + V(z)j
Navier-Stokes equation:
dV/dt + (V.del)V = g - (1/ro)*(del)(p) + v(del^2)V
p>Solution