If the laminar velocity profile is approximated by the cubic-order polynomial where, a = u/U, and y = y/8 with U, and 6 being the edge velocity and boundary-layer thickness, respectively. a) Find out the velocity profile, by determining the unknown coefficients a,, a,, a, and a,. Plot the velocity profile. b) Find out the analytical expression for the boundary layer, displacement and momentum thickness and also find out their stream-wise variation as a function of x. Specifically prove that 8/x = 4.64/Re,, 8./1 = 1.74/VRe, and 0/r = 0.646//Re,

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Fluid Dynamics

The study of the flow of gases and liquids, usually in and around solid surfaces, is known as fluid dynamics in physics and engineering. Fluid dynamics, for example, can be used to evaluate the movement of air through an airplane wing or the surface of a vehicle. It can also be used in ship design to increase the speed at which ships pass through water.