Fundamentals of Fluid Mechanics B Assignment 8 — Boundary Layer
 Instructions
Write your solutions in single column format, with one statement following another vertically. Write your solutions neatly so that they are easy to read and verify. Don't write one line with two equal signs. Highlight your answers using a box. Failure to do this will result in a lower score and fewer comments on my part.
 04.18.20
 Question #1
Starting from the velocity distribution expression obtained through a polynomial fit through the boundary conditions, calculate all components of the vorticity vector within a constant pressure boundary layer over a flat plate at a certain $x$ distance from the leading edge. Plot the vorticity as a function of the $y$ coordinate. Are the results in accordance with the rates of vorticity input to the flow at the wall seen in class? $$\frac{\partial \vec{\omega}_z}{\partial y}=-\frac{1}{\mu}\frac{\partial P}{\partial x}$$ $$\frac{\partial \vec{\omega}_x}{\partial y}=\frac{1}{\mu}\frac{\partial P}{\partial z}$$ Why or why not? Explain.
 Question #2
You perform an experiment in which liquid water at a temperature of 27$^\circ$C flows on a flat plate as follows:
The flat plate has a length $L$ of 2 meters, a height $H$ of 2 mm, and a depth $D$ of 1 meter. Knowing that the boundary layer thickness at the trailing edge of the plate is of $\delta=2.76$ cm, estimate as well as possible the total drag force on the plate caused by the flowing water. Please use the following data for liquid water: density $\rho=1000$ kg/m$^3$, viscosity $\mu=10^{-3}$ kg/ms, heat capacity $c=c_p=c_v=4200~$J/kgK, conductivity $k=0.6~$W/mK.
 $\pi$