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Unformatted text preview: Exam 3, Spring 2008 page 1 Problem 1 (12 points) (020) e ’1’:
A. (1 point) Draw an xy coordinate system on the If/
drawing to the right. H _ _ _ r“ J? Speciﬁc
‘t/ weight of the ‘ fluid =7
B. (7 points) Find the resultant force FR on the
submerged rectangle and the location where it acts (KR, 3/12) in terms of y, 6, d, b, and a. ,r' \ Put boxes around your final answers. I” Exam 3, Spring 2008 page 2 You can use the top part of this page to work on Problem 1
Please put a box around your ﬁnal answers A P :5" (ﬁts 'Qw’ 7 K
G'f‘CLC‘M‘V'f’G Ck, 2 e 2 55a: TAN?) in YEW“ t~ ..s  rywbx\tL’L.
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TS? {tart cit (AlWk 0"?“va +\ Scar Y‘ww“ (1 {tarcab magi» 3}; Cﬂ'i"mlb‘l“lﬂ. C (4 points) Here is the front View of the same rectangular plate, redrawn below the surface.
The centroid is labeled "C". The six dots on the plate indicate six possible locations for (X3, yR). Label that vertical line H.
What is the value of H in terms of yR? 7 V
If you are confused, go back and look at the coordinate system you drew in part A} “Fig; No PC Draw a vertical line from the surface of the water to the correct location of (KR, wig 2 F +3 N 0 PC. ., f:
a “a 2 “la
' E 'i 1A9 H Exam 3, Spring 2008 page 3 Problem 2 (8 points): The drawing below shows a dam filled with water with specific weight y.
The top of the dam is open to the atmosphere. Notice that the location of y = O has been indicated in the drawing on the right. The shape of the dam is given by the equation y = IAX4
where A is a constant. it = u. ' H ‘{
Side View H Front View T A (4 points) Write a double integral to find the magnitude of the force due to pressure acting on
the wall of the dam that is in contact with the water. Make the outside integral with respect to
the variable x. You do not need to solve the integral. You will be graded only on how you set it up, including limits of integration. Use gage pressure to express your answer. tr: game e: e/ +~ ﬂatbed Z a +3
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5qu O 3%“ 1H d
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V” it K4) a B (4 points) Write a double integral to find the magnitude of the force due to pressure acting on the wall of the dam that is in contact with the water. Make the outside integral with respect to
the variable y. You do not need to solve the inte ral. You will be graded only on how you set it up, including limits of integration. Use gage pressure to express your answer. em
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Bi— Exam 3, Spring 2008 page 4 Problem 3. (3 points, no partial credit) You are designing a hydraulic lift for a mechanic‘s
shop. You plan to use a piston with a radius of 5 inches. What is the maximum fluid pressure
you will need to ensure that the maximum lifting capacity of the lift is 10,000 lbf? Remember units. u—mmm..m_.___m0_, N. . F _r 10(535'13 9‘ ‘1} W (no Q
{E} REL Karl" , 4f is B
‘ K ugh/C '3 F "L 8'9 ELR \Rxwmmu. [0 [6110 m: _—, to (is) (2;, metal} _r...4—————m~— L, .. ._ P: is, .: anal
"25“? W 'rrr l“ Problem 4. (4 points) The parallel plates shown below have a ﬂuid between them and are
separated by a distance of 4 mm. A shearing stress of 100 Pa develops at the upper plate when it
is pulled at a velocity of 2 meter/second. Assuming a linear velocity profile between the plates, what is the dynamic viscosity of the ﬂuid? Write your answer in this box, being sure to include
units in terms of kilograms, meters, and seconds Exam 3, Spring 2008 page 5 Problem 5. 14 points
Hint: Remember that free body diagrams typically help when solving problems. An empty cylindrical can is ﬂoating in the ocean. The ocean water has a density of pr
The can has mass Mm, radius R, and a total height H. A. (6 points) Find the height Habm,e of the can that sticks above the water. (BMW 22:0(KMM9 v m WW7 7’: Mllewt CK P e “T R7" r =_\ .._..t___n___m_u M , _b_w___..t_.ix
B. (8 points) Now someone comes along and pours some sodapop into the can. The soda has
density p5. What is the height of the soda in the can when the top of the can is exactly level with the surface of the ocean? W
QMNv : U‘W + ﬂights) 06 : thwe goo} em) % MWM# _ m‘w%§?ar wmfw*mﬁg
H5 3&Q__ p E ___W_M_m,__m_~._.l_.1.‘_.mw w M v: x
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This note was uploaded on 09/29/2008 for the course MECH 241 taught by Professor Hartmann during the Spring '08 term at Northwestern.
 Spring '08
 HARTMANN

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