ME 106 HW 5 Solutions

ME 106 HW 5 Solutions - University of California Berkeley...

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Unformatted text preview: University of California, Berkeley Mechanical Engineering Prof S. Morris ME106 Fluid Mechanics, Problem Set 5 1. (Review problem) Solve the problem studied in Lect 9 by working in Cartesian coordinates. The velocity V is then given by V = − ( ¡ y i + x j ). (a) Find the Cartesian components of the acceleration a , and show that r£ a = 0. (b) Show that the three components of Euler's equation are ½x − 2 = @p @x ; ½ y − 2 = @p @y ; 0 = @p @z + ½g: Hence ¯nd the pressure, and the equation of the free surface. 2. Find the value of the constant c for which the axisymmetric velocity ¯eld in which V = kr ^ r + cz ^ z satis¯es the continuity equation for incompressible °ow. 3. ( Squeeze ¯lm °ow ) The ¯gure shows a rigid disc of radius R moving with uniform velocity ¡ V ^ z towards a stationary plane surface at z = ¡ h . The gap between the disc and plane is ¯lled with an incompressible liquid. As the disc moves downwards, the liquid is squeezed from the gap. At distance r from the symmetry axis, the radial component of liquid velocity is given by v r = U ( r )(1 ¡ z 2 =h 2 ), where the function U ( r ) is to be determined, but is known to vanish at r...
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This note was uploaded on 04/29/2008 for the course ME 106 taught by Professor Morris during the Spring '08 term at Berkeley.

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ME 106 HW 5 Solutions - University of California Berkeley...

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