1. A 2-dimensional (x-y), steady, incompressible flow is described by Cartesian velocity components u, v: u...

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1. A 2-dimensional (x-y), steady, incompressible flow is described by Cartesian velocity components u, v: u = x and v = -y. o Write a concise, technically precise, verbal description of how the velocity components u and v vary with x and y. Consider only the upper right-hand Cartesian quadrant (region x>0, y> 0). o Sketch some streamlines in the upper right-hand Cartesian quadrant (region x>0, y> 0). Demonstrate that the proposed flow velocity field satisfies the conservation of mass law. o Find the potential function corresponding to the proposed flow velocity, and demonstrate that this potential function satisfies the potential flow equation (zero Laplacian). Demonstrate that the proposed flow velocity field satisfies the viscous (Navier-Stokes) equations. o What is the equation describing the variation in PRESSURE for this flow? DISCUSSION: What feature of the given velocity function allows it to satisfy both the viscous and inviscid equations? What real flow situation do the streamlines and velocity components suggest? 1. A 2-dimensional (x-y), steady, incompressible flow is described by Cartesian velocity components u, v: u = x and v = -y. o Write a concise, technically precise, verbal description of how the velocity components u and v vary with x and y. Consider only the upper right-hand Cartesian quadrant (region x>0, y> 0). o Sketch some streamlines in the upper right-hand Cartesian quadrant (region x>0, y> 0). Demonstrate that the proposed flow velocity field satisfies the conservation of mass law. o Find the potential function corresponding to the proposed flow velocity, and demonstrate that this potential function satisfies the potential flow equation (zero Laplacian). Demonstrate that the proposed flow velocity field satisfies the viscous (Navier-Stokes) equations. o What is the equation describing the variation in PRESSURE for this flow? DISCUSSION: What feature of the given velocity function allows it to satisfy both the viscous and inviscid equations? What real flow situation do the streamlines and velocity components suggest?

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The given 2dimensional steady incompressible flow has velocity components described by u x and v y Heres a stepbystep analysis based on the tasks a Description of the Velocity Components The velocity ... View the full answer