Consider the rotor blades of a helicopter, which rotate at an angular velocity, , and have radial length, R, and width, L (see figure). Assume that the blade is flat, has negligible thickness, and is aligned parallel to the flow. (a) Assuming a turbulent boundary layer, derive an expression for the total friction drag force on the blade. While there is no exact theory for turbulent flow over a plate, the turbulent boundary layer thickness is thought to depend on Rex according to the formula (where x is the distance from the leading edge of the plate): (x)0.37xRex1/5 and the wall shear stress is given by: w=0.0288U2Rex1/5 (b) In part (a) you assumed that the boundary layer was turbulent. However, the boundary layer i s actually laminar until Rex exceeds approximately 2105, after which it transitions to a turbulent boundary layer. Show by means of a calculation at r=R/2, if it is a good approximation to assume that the flow over the entire blade was turbulent. Use the given properties of air at 25C and the dimensions of a typical helicopter (given in figure)