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A high-viscosity oil is transported through a wide rectangular duct of length L, width W and...
A high-viscosity oil is transported through a wide rectangular duct of length L, width W and depth 2B via pressure-driven flow. The duct is inclined at an angle b? below the horizontal plane (gravity may be assumed to act downwards in the vertical direction), and is sufficiently broad that edge effects may be neglected in the transverse (x2) direction. The pressure at the upstream end of the duct (x1=0) is Po, and at the downstream end (x1=L) is PL. The flow may be regarded as laminar and isothermal, and the oil is a Newtonian liquid;? the duct may be regarded as stationary.
(a) Starting with the appropriate form of the Continuity Equation and Equations of Motion derive an equation for determining the x1 component of velocity at steady state. Be sure to identify all assumptions and boundary conditions. You should attach a marked equation sheet showing the manner in which you simplified the Navier- Stokes Equations.
(b) Derive an equation for the volume flow rate of oil through the duct at steady state under these conditions.
(c) Derive an expression for the shear stress T31 at the upper surface of the duct (x3 = B) at steady state.
Solutions
Amanda K answered 2 years agoRelated Solutions
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