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CENTER OF PRESSURE MEASUREMENT EXPERIMENT

OBJECTIVE

The objectives of these experiments are for student to study and determine the center of

pressure of a totally or partially submerged plane surface.

Determination of centre of pressure

Comparison of the centre of the pressure measurement with theoretical position

THEORY

Figure 1: Free ody Diagram of the !pparatus

The center of pressure is the point on a body where the total sum of the aerodynamic

pressure field acts" causing a force and no moment about that point

The hydrostatic pressure is calculated from:

#here $ is fluid density"g is gravity acceleration and h is the distance from li%uid free

surface. ecause no shear stress exists in a static fluids" all hydrostatics forces on any elements

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of a submerged surface must act in a direction normal to the surface. !bove e%uation shows

that pressure distribution varies linearly over inclined surface. The resulting forces acting on

the surface is related to the pressure of the centered of the surface" &c and the surface area" !:

#here &c itself is related to the depth of center of the area of the surface of the hc. The

resultant force is not therefore applied on the centered of the surface and the point of action of

the resultant force is named as center of pressure. Center of pressure of a surface can easily be

found using a balance of moments.

Y

'( is referring to the distance of resultant force that acting on center of pressure to the

surface of the water. )xc is a second moment of inertia. 'c is the distance from the center of the

geometry to the surface

Figure 2: Determination of moment about the axis above water surface

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Where :

* inclined angle to the vertical" which is subjected to the action of an increasing depth of

water.

+ depth of water above the lower edge of the rectangle.

(1 slant distance from the axis , to the upper edge.

(- slant distance from the axis , to the lower edge.

( slant distance to the water surface.

width of the rectangular plate.

y slant distance.

/y slant length.

First" consider the moment produced by the action of hydrostatic pressure on an element with

the slant distance of y and slant length of /y" therefore" the area of the element"

A= b y.

The depth of element below the water surface is (y - R4) cos " thus the hydrostatic pressure" p

on it is

p 0 wy 2 (3 cos *

The hydrostatic force" /F on the element is

/F 0 p/! 0 wby 4 (3 cos */y

This force acts at radius y from the axis at 5" as a result" the moment /6 produced about 5 is

/6 0 wby y 4 (3 cos */y

The total moment 6" obtained by integration over the submerged area"

6 0 wb cos * (y R)dy

The limits of integration over the submerged area are different for partially submerged and

fully submerged.

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Figure 7: &ressure Forces on a &lane 8urface

(eferring to figure 7" consider an element at start depth y" width /y

Case ! P"a#e F$""y S$%&e'e

9imit (1and (-

( (1and

5r

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Case *! P"a#e Pa'+,a""y S$%&e'e

9imit (1and + sec *

(; (1and

APPARATUS

Figure 4: The entre of !ressure A""aratus

9egend:

! 0 (ight hand side tan