Winter 2007
BIEN 301
533568723
Page 1 of 11
BIEN 301
Winter 2006-2007
Exam 1
Part 2 of 2
(60 points, 78 possible points, approximately 60 minutes)
Instructions:
1. The work must be your own original work, no outside help or collaboration
permitted.
2. The honor code statement must be signed on each one of these sheets by writing
your name and date in the appropriate location.
3. As much as possible, list references for where you obtain information. Equations,
facts, tables, conversion factors, etc. Quality points will be considered for wellreferenced, neatly worked exams when trying to decide borderline grades.
4. All the other exam stipulations as listed in lecture apply: List out your
assumptions, sketch the problem, state specifically what you are seeking to
find/solve. Show your work, box your answers. Follow the instructions for each
individual question.
5. The “Relevance to Biomedical Engineering statement” requirement, as well as the
“Full Problem Restatement” requirement are not expected for the work here.
6. For actual problems to be worked out, the confidence check may be used. The
confidence check is OPTIONAL. If you are CERTAIN your work is 100%
CORRECT, you can mark the confidence check line with a “YES”. If you are
indeed correct, you will receive bonus points on that question. If you marked
“YES” and are incorrect, you will get the partial credit due to you, MINUS the
listed points. NOT marking the box will not benefit or penalize you. It is purely
your choice.
7. Extra credit is exactly that, extra credit. Working a problem and getting it wrong
will not hurt you, you can only gain points. However, Confidence Check (item 7,
above) rules WILL apply.
8. Total points you will be graded on for both parts 1 and 2: 100. Total POSSIBLE
points: 129 points. Plenty of extra credit/confidence checks opportunities.
9. Select a question, indicate your selection, and proceed to solve the question.
Student Name:
Date:
Honor Code Statement: “Being a student of a higher standard, I pledge
to embody the principles of academic integrity.”
Winter 2007
BIEN 301
533568723
Page 2 of 11
Question 1 (20 points) Select one of the following:
Q1a) The quantities viscosity μ, velocity V, and surface tension Υ may be combined into
a dimensionless group. Find a dimensionally homogenous solution that is proportional to
viscosity μ.
or
Q1b) Given the following formula for the volume flow rate, Q, of a liquid through a hole
of diameter D in the side of a tank:
Q  0.68D 2 gh
Where g is the acceleration due to gravity and h is the height of the liquid surface
above the hole. Find the dimensions for the constant, 0.68, to maintain dimensional
homogeneity.
Question Selected_____
Confidence Check for Question 1 (+ or - 4 points)____
Solution:
Student Name:
Date:
Honor Code Statement: “Being a student of a higher standard, I pledge
to embody the principles of academic integrity.”
Winter 2007
BIEN 301
533568723
Page 3 of 11
Student Name:
Date:
Honor Code Statement: “Being a student of a higher standard, I pledge
to embody the principles of academic integrity.”
Winter 2007
BIEN 301
533568723
Page 4 of 11
Student Name:
Date:
Honor Code Statement: “Being a student of a higher standard, I pledge
to embody the principles of academic integrity.”
Winter 2007
BIEN 301
533568723
Page 5 of 11
Question 2 (20 points) Select one of the following:
Q2a) A shaft 3 cm in
diameter is being pushed
axially through a bearing
sleeve 3.01 cm in diameter
and 20 cm long. The
clearance, assumed
uniform, is filled with oil, v
= 0.003m2/s and SG =0.88.
Estimate the force required
to pull the shaft at a steady
velocity of 0.2 m/s.
Or
Q2b) A solid cylinder of
diameter D=4cm, length
L=30cm, and density ρs=7850
kg/m3 falls due to gravity inside
a tube of diameter D0=4.04cm.
Assuming even distribution of
the clearance, the clearance is
filled with a lubricant with a
viscosity μ = 0.29kg/m-s. Find
the terminal velocity of the
steel cylinder.
Student Name:
Date:
Honor Code Statement: “Being a student of a higher standard, I pledge
to embody the principles of academic integrity.”
Winter 2007
Question Selected_____
BIEN 301
533568723
Page 6 of 11
Confidence Check for Question 2 (+ or - 5 points)____
Solution:
Student Name:
Date:
Honor Code Statement: “Being a student of a higher standard, I pledge
to embody the principles of academic integrity.”
Winter 2007
BIEN 301
533568723
Page 7 of 11
Student Name:
Date:
Honor Code Statement: “Being a student of a higher standard, I pledge
to embody the principles of academic integrity.”
Winter 2007
BIEN 301
533568723
Page 8 of 11
Question 3 (20 points) Select one of the following:
Q3a) Given a water tank,
20 cm in diameter by 40 cm
high, filled with water to
the 25 cm mark. The tank is
accelerated at 5m/s2 in the
direction shown.
Find:
a) the heights at the
surfaces indicated (h1, h2,
h3, and h4).
b) The error in pressure
measurement of the
pressures at the bottom of
the tank using the
manometers shown.
c)If all measurements
(including given values)
have an accuracy of 1%,
what is the true error?
Or
Q3b)
a)For what uniform rotation
rate (RPM) about the shown
axis will the fluid in the u-tube
take the configuration shown?
The fluid is glycerin at 120ºC.
b)If all measurements
(including given values) have
an accuracy of 1%, what is the
error for the calculated
rotation rate?
EXTRA CREDIT (4 points)
a) For what uniform rotation
rate will the fluid reach the
bottom of the right leg (as
shown in the figure)? b) How
high will the fluid in the left leg
be at this point?
Student Name:
Date:
Honor Code Statement: “Being a student of a higher standard, I pledge
to embody the principles of academic integrity.”
Winter 2007
Question Selected_____
BIEN 301
533568723
Page 9 of 11
Confidence Check for Question 3 (+ or - 5 points)____
Solution:
Student Name:
Date:
Honor Code Statement: “Being a student of a higher standard, I pledge
to embody the principles of academic integrity.”
Winter 2007
BIEN 301
533568723
Page 10 of 11
Student Name:
Date:
Honor Code Statement: “Being a student of a higher standard, I pledge
to embody the principles of academic integrity.”
Winter 2007
BIEN 301
533568723
Page 11 of 11
Student Name:
Date:
Honor Code Statement: “Being a student of a higher standard, I pledge
to embody the principles of academic integrity.”