(a) Average rate of rotation of two line segments at +/- 45 degrees (b) Show that this is the same as in the example Problem 5.84 [Difficulty: 3] Given: Viscometric flow of Example 5.7, V = U(y/h)i, where U = 4 mm/s and h = 4 mm Find: Solution: We will apply the definition of rotation to the given velocity field. V 2 1 Governing Equation: (Definition of rotation) Assumptions: (1) Steady flow (2) Incompressible flow Considering the lines shown: u c u a y u l sin θ 1 ω ac u c u a sin θ 1 l since the component normal to l is u sin θ 1 ω ac y u l sin θ 1 sin θ 1 l y u sin θ 1 2 U h sin θ 1 2 Now consider this sketch: u b u d y u l sin θ 2 ω bd u d u b sin θ
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