Unformatted text preview: c) From the equation of continuity, show that the velocity in the x direction is a function of only t and y . d) Simplify the x component of the equation of motion. (Hint, you may assume there is no change in pressure with x .) e) What are the boundary and initial conditions? f) Use the transform η = y 4 nt to simplify the equation to an ordinary differential equation. Recall that the kinematic viscosity is ν = μ ρ . g) Use reduction in order and integrate twice to conclude v x V =1erf y 4 nt ae è ç ö ø ÷ where erf f ( ) = 2 p exp f 2 ( ) f ò df , and erf (¥ ) =1...
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 Spring '08
 Meredith
 Fluid Mechanics, Derivative, Fundamental physics concepts, Navier–Stokes equations

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