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ME218 hw7_2011

# ME218 hw7_2011 - An airplane is being tracked by a radar...

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ME 218: ENGINEERING COMPUTATIONAL METHODS Home Work #7 Assigned: October 21, 2011 Due: October 27, 2011 Name: __________________UT EID: ____________Unique: _________ Lab Time: (Mon/Tue) ___PM Problem 1: Least Squares Method (Exponential) Andrade’s equation has been proposed as a model of the effect of temperature on viscosity: a T B D / e = μ where μ =dynamic viscosity of water, a T = absolute temperature (K), and D and B are parameters. Fit this model to the following data for water. ) ( C T 0 5 10 20 30 40 ) / 10 ( 2 3 m Ns × μ 1.787 1.519 1.307 1.002 0.7975 0.6529 Note: ] [ ) 273 ( ] [ C T K T a + = Problem 2: Numerical Differentiation (Forward / Backward)
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Unformatted text preview: An airplane is being tracked by a radar, and data is taken every two seconds in polar coordinates θ and r. t (s) 200 202 204 206 208 210 (rad) 0.75 0.72 0.70 0.68 0.67 0.66 r (m) 5120 5370 5560 5800 6030 6240 Calculate the velocity of the plane as a function of time, where the velocity V is given by: ( ) 2 2 r V r + = Compute the derivatives using the appropriate finite difference techniques (forward, central or backward difference – what ever is the best at any given point). Note that here dt d and dt dr r = = ....
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