Unformatted text preview: v x and v y , as well as the cylindrical components v r (radial component) and v θ (tangential coordinate). Assign numerical values to all components. 4. The flow of a fluid past a wedge is described by the potential ψ ( r, θ ) = − cr α sin αθ , where c and α are constants, and ( r, θ ) are the cylindrical coordinates of a point in the fluid (the potential is independent of z ). Verify that this function satisfies Laplace’s equation, ∇ 2 ψ = 0 . 5. Expand the function y ( x ) = e x sin x in a Taylor series about x = 0 , keeping the first 2 nonzero terms. 6. Solve the ordinary differential equation (cylindrical coordinates) 1 r d d r ± r d v z d r ² = C, where C is a constant, subject to the boundary conditions v z = 0 at r = κR (0 < κ < 1) , v z = 0 at r = R. Here, κ and R are also constants. 1...
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- Spring '10
- Derivative, Coordinate system, Polar coordinate system, Coordinate systems, Cylindrical coordinate system