quiz_2_04_sol - Ain Sonin and Gareth McKinley Solutions to...

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Ain Sonin and Gareth McKinley Solutions to Quiz 2 2.25 Fall 2004 Problem 1 The transition from dripping to jetting See C. Clanet & J. Lasheras, “Transition from Dripping to Jetting”, J. Fluid Mech 383 , 1999 p307 for more details on this problem! Figure 1 Figure 2 (snapshot at a single instant in time t ) For fluids exiting from typical size orifices, viscous stresses are negligible because a dimensionless parameter known as the Ohnesorge number is small. This is defined as Oh = μ ρσ D . For the case here we thus have Oh 10 3 10 3 (0.07)(0.005) 0.0017 ! (a) The surface is cylindrical and there is no tangential stress (no viscous effects). Normal to the jet we have pressure and surface tension acting. The principal radii of curvature for a cylinder are such that the mean curvature is given by: 2 H = 1 R a + 1 R b = 1 ( D 2) + 1 = 2 D (1) hence p i n = p a + 2 H σ ( ) n p i = p a + 2 D (2) The additional axial force arising from surface tension acting along the axial direction of the jet is F z = π D (remember surface tension is a line force – proportional to length). (b) Criterion: The flux of momentum into the control volume shown must always be greater than zero (otherwise a stationary pendant drop will have formed which is attached to the orifice). The ‘A form’ of the conservation of linear momentum is most appropriate; this gives d P cv dt + ρ v ( v-v c ) n dA CS ( t ) = F cv (3) g A B U = Q 4 D 2 ( ) L
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2.25 Fall 2004 Quiz 2 2 For the z-component
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quiz_2_04_sol - Ain Sonin and Gareth McKinley Solutions to...

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