5 the velocity profile where v ui v inside the thin boundary layer ove

Question

5. The velocity profile (where V = uî + vĵ ) inside the thin boundary layer over a flat plate is given as,
u=V_{0}\left[\frac{2}{2}\left(\frac{y}{\delta}\right)-\frac{1}{2}\left(\frac{y}{\delta}\right)^{3}\right] ; \quad 0 \leq y \leq \delta \delta=5 \sqrt{\frac{\mu \tau}{\rho V_{0}}} To answer the parts below, assume that the y-component of velocity within the boundary layer is very small compared to the î– compotent; i.e. u >> v. (a) Find an expression for shear stress Tyr acting on the plate as a function of the position X. (a) Find an expression for shear stress Tyr acting on the plate as a function of the position (b) Using the shear stress expression, compute value of the non-dimensional drag force (called as drag coefficient) on the plate of length L and width W and defined as \text { Drag Coefficient }=\frac{\text { Net Drag Force }}{\left(\frac{1}{2} \rho V_{0}^{2}\right)(L W)} ) Find an expression for the vorticity component w, in the z direction as a function of ä and y. Is the flow rotational or irrorational? e) If a small square fluid element is placed within the boundary layer, sketch its shape as the fluid element moves downstream with the flow.