1. Consider a steady state two-dimensional fluid flow with only two components of velocity, x-component (vx) and y-component (vy) (i.e. there is no z-component of velocity, v₂ = 0): v = (ax+b)ex + (-ay + cx)ey. Assume that gravity force does not act in x and y direction. a) Show that this velocity field satisfies the equation of continuity for an incompressible fluid. b) Use Navier Stokes equation to show that for this fluid flow pressure gradient exists in both x and y direction. c) Show that P (pressure) is a continuous function of x, and y. (Hint: For a continuous smooth function, the cross derivative of the function is equal, i.e. differentiation with respect to more than one variable yield results that are independent of the order in which the derivatives are taken) 2R

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