MEEN 344: Section 502 HW Problem Set #5 (Due on 10/10/06) 1.For a flow in the xy plane, the x component of velocity is given by()uAxyB=−, where A = 2 m-1s-1, B = 2m, and x and y are measured in meters. Find a possible y component for steady, incompressible flow. Is it also valid for unsteady, incompressible flow? Why? How many y components are possible? 2. Consider the velocity field 22ˆˆ(2)(2)VAx xyiAxyyj=+−+Gin the xy plane, where A = 0.5 m-1s-1, and the coordinates are measured in meters. Is this a possible incompressible flow field? Calculate the acceleration of a fluid particle at point (x,y) = (2,1). 3.Consider the incompressible flow of a fluid through a nozzle as shown below. The area of the nozzle is given by 0(1)AA bxand the inlet velocity varies according to 0)tUUeλ−, where A0 = 1 m2, L = 5 m, b = 0.1 m-1, λ= 0.1 s-1, and U0 = 5 m/s. Find and plot the acceleration on the centerline, with time as a parameter.
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