A steady two-dimensional flow of a constant density fluid in the horizontal plane is described by: V = -2xy i + (y? -x²)} a) Determine if the continuity equation is satisfied? b) Determine the fluid acceleration å at point (x, y) = (0.5 m, -0.5 m). c) Determine the vorticity at point (0.5 m, -0.5 m). d) Determine the stream function (x, y) for this flow field. e) Determine the equation of the streamline passing through the point (0.5 m, -0.5 m). f) Determine if the given velocity field is a realistic solution to the Navier-Stokes equations when gravity effects are neglected. g) Determine, if possible, the pressure field P(x, y) if the pressure at point (0,0) is known to be Po- h) Determine, if possible, the stress tensor components Oxx, Oyy, and oxy at point (0.5 m, -0.5 m) with Po = 0.25 Pa, u = 0.25 Pa s, and p = 4 kg/m3. Hint: Stress tensor can be expressed as oij = -Pôij + tij (i,j = x, y), where dij is the Kronecker delta and Tj is the viscous stress tensor.

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Frames

The trusses and frames are the two most important structural members of civil engineering. Trusses are the interconnection of links and other structural members. The interconnection with other members makes the system behave as a single member that supports and transfers loads. Trusses are generally two types, plane truss, and space truss. Frames on the other hand form the skeleton of any building construction. Frames are structures formed by the connection of beams, columns, slabs, and joists. These members provide the building with the required structural support.