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newassign2 - FLUID MECHANICS II Assignment 2 Question 1 a)...

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Unformatted text preview: FLUID MECHANICS II Assignment 2 Question 1 a) By following the motion of a fluid parcel in a two-dimensional, planar flow (parcel moves from (x,y) to (x+∆ x, y+∆ y) in time ∆ t), show that Lagrangian and Eulerian acceleration in 2 D (a = axˆ + ay ˆ) are i j related by Du(t) ∂u ∂u ∂u = +u +v , Dt ∂t ∂x ∂y Dv (t) ∂v ∂v ∂v ay = = +u +v , Dt ∂t ∂x ∂y ax = where u, v on RHS are the Eulerian velocities, i.e. u(x, y, t) = u(x, y, t)ˆ + v (x, y, t)ˆ i j. b) Work out the corresponding connection between the parcel rate of change of temperature the Eulerian temperature field T(x,y,t). DT (t) Dt and Question 2 By expanding out the vector equality a= Du(t) ∂u = + (u. )u, Dt ∂t where = ∂ˆ ∂ˆ ∂ˆ i+ j+ k ∂x ∂y ∂z work out the three-dimensional equivalents of 1(a); i.e. find ax , ay and az in terms of Eulerian quantities. Question 3: Problem 4.2 Question 4: Problem 4.3 a)b)d) Question 5 Suppose that the temperature field T = 4 x2 − 3 y 3 , in arbitrary units, is associated with the velocity field of Prob 4.3. Compute the rate of change dT at (x, y ) = (2, 1). dt Question 6: Problem 4.6 Question 7: Problem 4.8 Question 8: Problem 1.80 Consider only the lower portion of the positive quadrant. Plot up the following two streamlines: i) the streamline that passes through (0,0). ii) the streamline that passes through (2,1). A small particle moves along the fluid. Find its velocity and acceleration as it passes through (2,1). ...
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This note was uploaded on 09/14/2011 for the course ME 362 taught by Professor Ceciledevaud during the Winter '11 term at Waterloo.

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