Transport Phenomena · Local conservation laws, constitutive fluxes, and scaling
A Newtonian oil of density 860 kg/m^3 and viscosity 0.145 Pa s flows steadily through a…
Problem
A Newtonian oil of density 860 kg/m^3 and viscosity 0.145 Pa s flows steadily through a horizontal rectangular duct 12 mm high and 0.60 m wide. The width is sufficiently large that sidewall effects may be neglected. The pressure decreases by 18.0 kPa over a duct length of 4.00 m. Assuming fully developed laminar flow and no slip at both walls, determine (a) the velocity profile across the gap, (b) the volumetric flow rate, (c) the wall shear stress at each wall, and (d) the rate of mechanical-energy dissipation per unit duct length.
Hint
Treat the wide duct as two infinite parallel plates separated by (h).
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