To locate the center of pressure of an immersed rectangular surface and to compare this position with that predicted by theory.
Apparatus
The following equipment is required for this experiment:
Figure 1.1.
Theory
The magnitude of the total force F, acting on the face of a torroid is given by:
A = area of the rectanglar face (2 7/8" x 4"),
p = density of water,
g = acceleration due to gravity, and
hc = depth of centroid G below surface of water = d1 - ½(depth of rectangular section)
Theoretical Determination of the Center of Pressure xp:
Theory shows that
IG = 2nd moment of area of the immersed surface about the horizontal axis passing through the centroid
The equation for the second moment of area of the immersed surface about the horizontal axis is:
b = breadth of the rectangular section, and
d = depth of the rectangular section
Experimental Determination of xp:
For equilibrium of the apparatus, moments about the pivot give:
F = pressure force
y = distance from pivot to centre of pressure
m = mass added to hanger, and
s = distance from pivot to hanger.
Therefore
but
where
Therefore
R1 = distance from pivot to bottom of rectangular surface, and
d1 = depth to water surface from bottom of rectangular surface
Experimental Procedure
The following procedure is to be performed during this experiment:
Report