Last Rev.: 11 JUN 08
Center of Pressure Lab : MIME 3470
Page 1
Grading Sheet
~~~~~~~~~~~~~~
MIME 3470—Thermal Science Laboratory
~~~~~~~~~~~~~~
Laboratory №. 8
CENTER OF PRESSURE
Students’ Names  Section №
POINTS
PRESENTATION—Applicable to Both MS Word and Mathcad Sections
GENERAL APPEARANCE, ORGANIZATION, ENGLISH, & GRAMMAR
5
ORDERED DATA, CALCULATIONS & RESULTS—MATHCAD
ON A SINGLEGRAPH, PLOT OF CP vs. h FOR ALL INCLINATIONS
ON SAME GRAPH, PLOT WETTED PLANE CENTROID vs. h
PERCENT DIFFERENCE BETWEEN CALCULATED &
EXPERIMENTAL MOMENTS
25
15
10
DISCUSSION OF RESULTS
WHERE DOES CP LIE W.R.T. WETTED CENTROID, WHY?
WHEN DO THEY COINCIDE?
DERIVE ONLY KLINE-MCCLINCOCK UNCERTAINTY FOR CP
CONCLUSIONS
ORIGINAL DATASHEET
TOTAL
COMMENTS
d
GRADER—
10
10
10
10
5
100
SCORE
TOTAL
Last Rev.: 11 JUN 08
Center of Pressure Lab : MIME 3470
MIME 3470—Thermal Science Laboratory
~~~~~~~~~~~~~~
Laboratory №. 8

R2
h2 
F  gB cos  2  hR2 
(3)

2
2 cos  

Similarly, an expression for the moment is found by
integrating Equation 2 between the same limits,
CENTER OF PRESSURE
~~~~~~~~~~~~~~
LAB PARTNERS: NAME
NAME
NAME
SECTION
№
EXPERIMENT TIME/DATE:
NAME
NAME
NAME
M  gB
OBJECTIVE—The purpose of this exercise is to experimentally
determine the center of pressure on a plane surface partially or
totally submerged in a liquid. The center of pressure is defined as
the point of application of the resultant hydrostatic force applied
on the plane. As the pressure varies with the distance from the
liquid free surface, the pressure center will not coincide with the
centroid of the plane. Thus the experiment also compares the
locations of the center of pressure with respect to the centroid.
R1
Case 1
(4)
R

 

R2
R2
 gB  cos  2  hR2    cos  1  hR1 
 

2
2

 


 cos  2

2
 gB 
R2  R1  hR2  R1 
 2

dy


R3
O
R2
h
R1
Figure 1—Schema and Photo of Center of Pressure Apparatus
THEORY—Refer to Figure 1, which contains a photograph and a
diagram of the experimental apparatus. In the figure, the differential
force, dF, is acting on the differential area dA = B dy, where B is the
width of the tank. This differential force is defined by
dF  g  y cos   h dA
 gB y cos   h dy
and the moment of this differential force about point O, dM, is
(2)
dM  gB y cos  hydy .
(1)
Case 1: Plane Partially Submerged (see Figure 1, Case 1)
The force on the plane is found by integrating dF from h/cos() to R2.
  y cos  h dy
h / cos 
R

 2
y2
 gB cos   hy 
2

 h / cos 

 
R2
h2
h 2 

 gB  cos  2  hR2    cos 

 
2

2 cos 2  cos  
 

(5)
R2

3
R1

3
y
  y cos  h ydy  gB cos
h
y2 

2 
R2
R1

R3
R 2 
R3
R 2 
 gB  cos  2  h 2    cos  1  h 1 
3
2  
3
2 



Case 2
R2
 cos 
R2  R1   h
F  gBR2  R1 
2


and
M  gB
y
dF
F  gB

R3
R2
h3 
M  gB cos  2  h 2 

3
2
6 cos 2  

1
dF
dy

R3
R 2 
h3
h 2 

 gB  cos  2  h 2    cos 

h
3
2

3
2  





3
cos

2
cos





 2
y2
F  gB   y cos   h dy  gB cos   hy 
2
R1

 R
h
y
Plane surface for which
the resultant hydrostatic force is desired
2

y3
y2 
 gB cos   h 
3
2 

h / cos 
R2
R2

W
  y cos  h ydy
h / cos 
Case 2: Plane Fully Submerged (see Figure 1, Case 2)
Integrate Equations 1 and 2 between the limits R1 and R2 to obtain
O

R2
R
TIME, DATE
~~~~~~~~~~~~~~
B is the width
of the tank
(into the page)
Cradle
Page 2

 

 cos  3

 h
(6)
M  gB 
R2  R13   R22  R12 
 2
 3

THE CENTER OF PRESSURE LOCATION, MEASURED FROM POINT O,
CAN BE DETERMINED BY DIVIDING THE MOMENT BY THE FORCE.
EXPERIMENTAL PROCEDURE—Water is contained in a quadrant of a semicircular tank assembly that it is allowed to rotate about
Point O (see Figure 1). The cylindrical sides of the tank have their axes
coincident with the center of rotation, Point O, of the tank assembly.
Therefore, the total fluid pressure acting on these surfaces exerts no
moment about that center. The only moment present is due to the fluid
pressure acting on the plane surface. This moment is measured
experimentally by applying weights, W, to a weight hanger mounted
on the semicircular assembly on the opposite side to the quadrant tank.
The moment-arm length for this weight is R3. A second tank, situated
on the same side of the assembly as the weight hanger provides a
trimming facility and allows different angles of equilibrium to be
achieved. The angular position of the plane, , and the distance to the
water’s surface, h, are measured respectively on a protractor scale
mounted on the tank and a linear scale on the back panel.
Last Rev.: 11 JUN 08
Center of Pressure Lab : MIME 3470
1. Before starting, be sure that the zero line on the back panel lines up
with the center of rotation and the zero degree line on the tank.
NOTE: The axle on which the experiment rotates was mounted
10mm too high and that amount should be added to h measurements.
2. Also, level the base plate.
3. With the quadrant tank empty, place a 50g weight on the weight
hanger. Pour water into the quadrant tank until zero balance is
reestablished. Record the weight and distance to the water’s free
surface, h.
4. Repeat this procedure increasing in 100g increments.
5. Empty the quadrant tank and remove all the weights.
6. Add water to the trimming tank until it balances at an angle
specified by the teaching assistant.
7. Repeat the Steps 3 through 5 for this new angle.
Page 3
In the report include the following:
Calculations
Make a single plot of center of pressure (CP) measured from the
center of rotation, point O, versus distance to the water surface,
h, for all inclinations considered. On the same plot, graph the
centroid of the wetted surface from the center of rotation vs. h.
Verify the calculated moment with the experimental moment
obtained from the weights by expressing the difference as a percent.
Discussion of Results
 Specify where does the center of pressure lie with respect to the
wetted centroid of the plane and why? In what case does one
expect them to coincide?
Assuming that the only error in the measurements is incurred by
the measurement of the distance to the water’s free surface, just
derive an uncertainty analysis for the center of pressure
calculation for Case 2 using the Kline-McClintock method
presented in the Jet Impact experiment. There is a separate
downloadable file describing the Kline-McClintock method.
Last Rev.: 11 JUN 08
Center of Pressure Lab : MIME 3470
ORDERED DATA, CALCULATIONS, and RESULTS
Page 4
Last Rev.: 11 JUN 08
Center of Pressure Lab : MIME 3470
DISCUSSION OF RESULTS
Specify where does the center of pressure lie with respect to the
wetted centroid of the plane and why?
Answer

In what case does one expect them to coincide?
Answer
Assuming that the only error in the measurements is incurred by
the measurement of the distance to the water’s free surface, just
derive an uncertainty analysis for the center of pressure calculation
for Case 2 using the Kline-McClintock method presented in the Jet
Impact experiment.
Derive here using Equation Editor
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CONCLUSIONS
Page 5
Last Rev.: 11 JUN 08
Center of Pressure Lab : MIME 3470
Page 6
DATA SHEET FOR CENTER OF PRESSURE
Time/Date:
___________________
Lab Partners:
_______________________
_______________________
_______________________
_______________________
_______________________
_______________________
Particulars of the Apparatus:
Inner Radius, R1:
___________ cm
Outer Radius, R2:
Lever Arm, R3:
___________ cm
Inside Tank Width, B: ___________ cm
Smallest Graduation of Measure of Distance to Free Surface, h
___________ cm
___________ cm
Moment Data at Various Inclinations:
0º Inclination
Mass Suspended
Distance to
from Hanger, m
Free Surface, h
(g)
(cm)
10º Inclination
Mass Suspended
Distance to
from Hanger, m
Free Surface, h
(g)
(cm)
20º Inclination
Mass Suspended
Distance to
from Hanger, m
Free Surface, h
(g)
(cm)
30º Inclination
Mass Suspended
Distance to
from Hanger, m
Free Surface, h
(g)
(cm)
d
d
d
d
d
d
d
d
d
d
d
d
d
d
d
d
d
d
d
d