Question

Consider a low speed, steady flow around the thn airfoil shown in figure below We know the velocity and altitude at which the vehicle is flying Thus, we know P. (ie, P) and U(ie. U) We have obtained experimental values of the local velocity U, U,U at Pots 2, 3 and 4 Pontat the stagnation point of airfoil Point 3 at a point in the inviscid region just Edge of boundary layer Point outside the thin boundary layer Point 4 at a point inside the boundary layer (a , Please evaluate the pressure P2 at Point 2? (6%) (bi Please evaluate the pressure Pi at Point 3"(6%) (c) Please evaluate the pressure Pa at Point 4 if the boundary layer thickness s thin, (7%)

Answer 1

3 Edge of boundary ayer 2 a Point 2 is stagnation poin U-0 Applying Bernoulli equation in inviscidreefon between İande 2 2 2 lies in inviscid regłon, hence Bernoulli equation fs applicable betioeen d and 3" 2. 2. 2 2 2 c Ir the boundary layer fs thin We can't compute P by applying Benouli as point 4" lies in the viscid Floro reglon breaking the most necessary assumption of Bemouli equation ressure across the boundary layer in ne constant ie This is because the boundary layer is so thin, streamlines within the boundary layer have negligble curvature ohen observed at the Scale oF boundary layer thickness urval strea m lines require a centripetal acelerati。ワroh?ch comes from a pressure radrent along the radius oF curvature. Since the stream-lines are not sig nificanty curved in a thin boundary layer, there is no signi ficant pressure gradient across the boundary layer