EAS4101_S11_HW8Q - EAS 4101 Aerodynamics Spring 2011 8th...

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EAS 4101 - Aerodynamics – Spring 2011 HW#8, 1/6 3/16/11, 8 th Homework 1. Given: 2 infinite plates, 2-D slot, with the stationary plate at 0 y and one plate moving at yh with a steady speed Consider that the flow is steady and fully developed. . p const 0 U h x y Find: a) Draw a schematic of this flow, clearly showing your coordinate system and list your assumptions for this problem. b) Simplify the Navier Stokes and continuity equations, clearly stating why each term is eliminated. c) List the boundary conditions for this problem. d) Solve for velocity component normal to the plates. e) Solve for velocity component parallel to the plates. f) Solve for the only non-zero shear stress component in this flow. g) Solve for the only non-zero vorticity component in this flow. 2. Given: 2 infinite plates, 2-D slot, with the both plates stationary at 0 y and at . There is a constant axial pressure gradient driving the flow, dp const dx Consider that the flow is steady and fully developed. h x y 1 p 2 p g constant dp dx Find: a) Draw a schematic of this flow, clearly showing your coordinate system and list your assumptions for this problem. b) Simplify the Navier Stokes and continuity equations, clearly stating why each term is eliminated. c) List the boundary conditions for this problem. d) Solve for velocity component normal to the plates. e) Solve for velocity component parallel to the plates. f) Solve for the only non-zero shear stress component in this flow. g) Solve for the only non-zero shear vorticity component in this flow. 3.
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EAS 4101 - Aerodynamics – Spring 2011 HW#8, 2/6 Given: A long, wide belt inclined at an angle with respect to the horizontal is submerged in a liquid of density and viscosity . The belt is moving with a steady speed U such that a thin film of liquid is pulled upward along the belt. Sufficiently far along the belt, the film possesses a constant thickness and the flow is fully developed. . p const Find: h) Draw a schematic of this flow, clearly showing your coordinate system and list your assumptions for this problem. i) Simplify the Navier Stokes and continuity equations, clearly stating why each term is eliminated.
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EAS4101_S11_HW8Q - EAS 4101 Aerodynamics Spring 2011 8th...

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