2020 Fundamentals of Fluid Mechanics A Midterm Exam
Thursday October 22nd 2020
11:00 — 12:15
 INSTRUCTIONS
 • NO NOTES OR BOOKS EXCEPT FOR THE FUNDAMENTALS OF FLUID MECHANICS TABLES. • ONLY A BAREBONE CALCULATOR IS ALLOWED WITHOUT SDCARD SLOTS OR A LARGE SCREEN. • ALL QUESTIONS HAVE EQUAL VALUE; ANSWER ALL 2 QUESTIONS. • WRITE YOUR SOLUTIONS IN SINGLE COLUMN FORMAT, WITH ONE STATEMENT FOLLOWING ANOTHER VERTICALLY. • ALWAYS START YOUR SOLUTIONS USING THE EQUATIONS IN THE TABLES. • OUTLINE ALL ASSUMPTIONS MADE. • WRITE YOUR SOLUTIONS NEATLY SO THAT THEY ARE EASY TO READ AND VERIFY. • USE A PENCIL OR A PEN WITH BLACK INK. DO NOT USE BLUE OR RED INK. • DON'T WRITE ONE LINE WITH TWO EQUAL SIGNS. • HIGHLIGHT YOUR ANSWERS USING A BOX. • SCAN YOUR SOLUTIONS USING CAMSCANNER AND CREATE ONE PDF FILE PER QUESTION. UPLOAD THE TWO PDF FILES ON THE D2L.
 10.21.20

 Question #1
Consider a water jet falling from a height $H=20$ m onto a blade as follows: Noting that the blade is moving downwards with the speed $q_{\rm blade}=10~$m/s, do the following:
 (a) Find the $x,~y,~z$ velocity components of the reflected water in the ground frame. (b) Find the force acting on the blade in the $z$ direction due to the water reflection.
You can assume that the pressure of the water far from the blade is equal to atmospheric pressure. Use $\theta=25^\circ$, $\phi=38^\circ$, $\dot{m}=10$ kg/s, $q_{\rm w}=30$ m/s, and $\rho_{\rm w}=1000$ kg/m$^3$. Outline clearly your assumptions.

 Question #2
Consider a tank filled with liquid water and air as follows: Knowing that $q_1=20$ m/s, $W_1=2$ cm, $W_2=3$ cm, $W_3=10$ cm, $H_1=3$ cm, $H_2=4$ cm, $\rho_{\rm air}=1$ kg/m$^3$, $\rho_{\rm water}=1000$ kg/m$^3$, do the following:
 (a) Derive a control volume form of the mass conservation equation that is applicable to either the volume $V_1$ or $V_2$. Note that, at the air/water interface, the surfaces $S_1$ and $S_2$ are moving. (b) Find $q_2$ by applying the expression derived in (a) to the volume $V_1$ and then to the volume $V_2$.
 $\pi$ 