CE 321
Lab # 1
FLUID STATICS
Experiment
yR 
Objectives:
I xc
 yc
yc A
Eq (1)
1. To experimentally verify the accuracy of Eq 1…..
a. Compare yR (exp) to yR theoretical
b. Look at actual error (yR theoretical- yR (exp))
2. To determine whether measurement uncertainty accounts for all the
inaccuracies.
a. Plot results, yR vs d (yR  2dyR)
b. Compare actual error to propagated error
c. Is uncertainty a major cause of inaccuracy?
3. Comment on the suitability of equation 1 over the experimental
approach.
a. Use the data from the above objectives
b. Try to relate physically the lab experiment to the “Real” world.
HINT: when writing your report keep objectives in mind, use them as the backbone or
structure
Mathematical Model
LOOK AT FIGURE 1 (blackboard)
After calibrating or zeroing the apparatus we can simplify the moment
equations to (note: this is just the simplified equation not the complete
moment equation)
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M pivot  0  FR ( L2 )  W ( L1 )
where
FR is the resultant force
L2 is the length of the arm where FR acts
W is the force produced by the mass placed on the tray
L1 is the length of the arm where W acts
Of all the terms in t he above equation L2 is the only unknown, all the others
are measured in the experiment.
L2 can then be calculated and used to determine our yR (exp) from
yR is the location on the submerged plane where FR is acting
L2 = yR +L3 – d  yR = L2 - L3 + d
Fully and Partially Submerged Planes
LOOK AT FIGURE 2 AND 3 (blackboard)
Pressure Prism
Location
Partially
Fully
Triangle
Trapezoid
2/3 height Somewhere
below water between 2/3
level
and 1/2
Equations for partially submerged are derived for you in the course pack.
Uncertainty
All measurements made have an uncertainty that accompanies them.
Example: scales and balances
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Measurements in lab are made with rulers; we will assume that they are
engineered to perfection.
Uncertainty “adds” itself from one measurement to the next. The process of
adding all the uncertainties is called propagation.
Equations for uncertainty are not simple need to be derived, squared and
then added.
For LAB
Objectives are reached by:
-
measuring FR, W, L1 and L3
finding L2 from sum of moments in the pivots
finding yR from the experimental equation
calculating yR from theoretical equation
compare yR experimental and theoretical
plotting yR experimental with its error bars (from propagation of
uncertainty), vs d.
Do measurement uncertainty dyR account for the inaccuracies?
GO TO LAB:
Lab Data sheets (hand -out)
Make sure to write down any observations of possible sources of error in the
lab, to help you answer objective 3.
Analysis:
A. Enter data in spreadsheet sent to you by email.
B+C. Plot the data on spreadsheet
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Lab # 1
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D. Actual error of yR calculations:
Absolute error: yR theo – yR exp
Relative error: (yR theo – yR exp)/ yR theo
E. What trends are in the data? Specifically look at partially submerged
vs. fully submerged
F. How does uncertainty affect dyR?
G. Are there any trends in the uncertainty?
H. Does uncertainty account for the inaccuracies found?
I. Use you engineering judgment to answer objective # 3
LAB REPORT:
1. Transmittal letter addressed to your TA. (Check format in coursepack)
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2. Abstract. May want to use the web to look up some abstracts and see
what is given in them. (Look for format in Techcom website)
3. Introduction: theory behind the experiment, objectives and purpose,
all equations should be here.
4. Methods and Materials (should include a sketch)
5. Results. Results are presented but not discussed
6. Discussion: all objectives should be discussed and answered with the
data; any conclusions should be backed-up with specific examples
from the data
7. Conclusions: Bulleted; 1 conclusion per objective; backed up with
data
8. Appendix: (datasheet from lab, references, additional sketches or
drawings, spreadsheet, sample calculations)
Old Lab Reports are available to look at not take home
Spreadsheet and Woksheets due on Thursday by 5 pm
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