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MAE 101A Summer I 2009 HW 4

MAE 101A Summer I 2009 HW 4 - thickness(no velocity...

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MAE 101A (Summer 2009) - Homework # 4 Due: Wednesday, July 29, 2009, at 6:00 pm (105 Center Hall) Problem 1: Solve Problem 4.1 of the textbook. Problem 2: The temperature distribution in a fluid is given by T = 10x + 5y, where x and y are the horizontal and vertical coordinates in meters, and T is in degrees Celsius. Determine the time rate of change of temperature of a fluid particle traveling: (a) horizontally with u = 20 m/s and v = 0; (b) vertically with u = 0 and v = 20 m/s. Problem 3: A two-dimensional velocity field V = (12xy 2 – 6x 3 ) i + (18x 2 y – 4y 3 ) j is given for a Newtonian, incompressible fluid, where the velocity has units of m/s when x and y are in meters. Determine the normal stresses xx and yy , and shear stress xy , at point (x, y) = (0.5, 1.0) if pressure at this point is 6 kPa and the fluid is glycerin at 20 C. Show these stresses on a sketch. Problem 4: A layer of viscous liquid of constant
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Unformatted text preview: thickness (no velocity perpendicular to the plate) flows steadily down an infinite, inclined plane. Obtain, using the Navier-Stokes equations, an expression for the flow rate per unit width in terms of , g, h, and . Assume air resistance is negligible, so that the shear stress ( yx ) at the free surface is zero. The flow is laminar. Problem 5: The three components of velocity in a flowfield are given by: u = x 2 + y 2 + z 2 , v = xy + yz + z 2 , w = - 3xz - z 2 /2 + 4 . Determine an expression for the angular velocity (rotation) vector, and find the vorticity. Is this an irrotational flow field? Problem 6: Determine the stream function corresponding to the velocity potential: = x 3 – 3xy 2 . Sketch the streamline = 0, which passes through the origin. Problem 7: Solve Problem 4.83 of the textbook....
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