Answer two questions and include all the steps with more explanations
Problem 1
Solve the Blasius equation for the velocity distribution on a flat plate using Runge-Kutta.
ζ''' + 1/2 ζζ'' = 0
Problem 2
For this problem, you are trying to design a hydraulic piston. For your hydraulic piston, you are using 2 concentric rods and fill the gap with a fluid. You plan to move the outer cylinder at a velocity U and keep the inner cylinder in a constant position. Develop a relationship that describes the velocity profile within the fluid. State your assumptions and boundary conditions.
