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:
M2020Q1.png  ./download/file.php?id=7171&sid=a7f3bc0774d44d768a5762babdee9884  ./download/file.php?id=7171&t=1&sid=a7f3bc0774d44d768a5762babdee9884
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:
M2020Q2.png  ./download/file.php?id=7172&sid=a7f3bc0774d44d768a5762babdee9884  ./download/file.php?id=7172&t=1&sid=a7f3bc0774d44d768a5762babdee9884
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 $V_2$.
PDF 1✕1 2✕1 2✕2
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