problem1a - c From the equation of continuity show that the...

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Name:_________________________________________ Problem # 1a ChBE 3200B, Spring 2006 1A. A large plate is initially at rest with a infinite fluid above it. At time t=0, the plate is put in motion at a constant velocity V in the x direction. The density and viscosity of the fluid are constant and gravity can be neglected. Determine the fluid velocity as a function of y and t . a) Write the Navier-Stokes equation for constant density and viscosity. Eliminate any terms that are not important. b) Select a coordinate system, and eliminate additional terms, You may assume that the velocity in the y direction, v y , is zero.
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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 =1-erf 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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