Abstract:The main objective of this experiment is to determine the center of pressure on a plane surface (rectangular surface) of the torroid by comparing the normal force (exerted by the liquid) and the weights on the balance bar.

Introduction: When a liquid is in contact with a solid surface, then two forces will beformed:1. Shear force: which is caused due to the viscosity of the liquid, and it describes the resistance of flow (friction) and depends on the type of the liquid. = (du/dy)Where: : Shear stress (Pa). : Viscosity (Pa.s). du/dy : Velocity gradient (1/s).

2. Normal force: it is caused from the weight of liquid on a plane around the surface, as dams and it acts on the surface as a line (normal to the area) and the centroid area of the surface.Sometimes we call the normal force, the pressure force.F = PA and in the case of a static fluid F = g hc A.Where hc: centroid.This relation is valid if the shape is rectangular and the plane surface is horizontal. For other shapes (rather than horizontal or rectangular) to find the centroid, evaluate the integral: dF = PdA.Where the pressure is linearly distributed over the surface.In this experiment the non-horizontal surface is also affected by the hydrostatic force due to the static liquid (water).Apparatus and Procedures : (a) Locate the torroid on the dowel pins and fasten to the balance arm by the central screw. (b) Measure the dimensions a, b, and d, and the distance L from the knife edge axis to the balance pan axis. (c) Position the perspex tank on work surface and locate the balance arm on the knife edges. (d) Attach a length of hose to the drain cock and direct the other end of hose to the sink. Attach a length of hose to tap V3 and place the free end in the triangular aperture on the top of the perspex tank. Level the tank, using the adjustable feet in conjunction with the spirit level. (e) Adjust the counter - balance weigh until the balance arm is horizontal. This is indicated on a gate adjacent to the balance arm. (f)Fill water to the perspex tank until the water is level with the bottom edge of the torroid. (g) Place a mass on the balance pan and fill water to the tank until the balance arm is horizontal. Note the water level on the scale. Fine adjustment of the water level may be achieved by over filling and slowly draining, using the drain cock. (h) Repeat the procedure under section. (g) for different masses : 5 masses for water levels y > d (complete immersion) and 5 masses for y < d (partial immersion) (i) Repeat readings for reducing masses on the balance pan.

Results and Discussion:

For the apparatus used, the formula:

And

May be applied to give expressions for the moment of the hydrostatic force about the knife-edge axis, where:

F: the water force of the torroid area. y: the centroid of the area. P: the water pressure at the centroid of the area. y: center of pressure. I: the second moment of the area.

* For Partial Immersion: yd (see fig.3)

Where:

and

The moment M of F about knife-edge axis for this case is given by:

Increasing:Mass (kg)Y(m)M/y (kg/m)

0.060.0222.73

0.080.03672.18

0.10.0551.82

Decreasing:Mass (kg)Y(m)M/y (kg/m)

0.050.015

0.060.0212.86

0.080.0362.2

Discussion:

It can be noticed that as the applied mass increases, the distances y and yc increase because the moment is needed for balance because the hydrostatic force exerted on the torroid increases.After finding the slope and intercept for both partial and complete immersion there were some deviations between experimental and theoretical values due to errors in measurements.

Conclusions and Recommendations:* In the case of a static fluid, the pressure force for the horizontal face can be calculated from the relationship: But for a non-horizontal shape the centeroid is found from the integration and then the pressure force (hydrostatic force) is evaluated.

* The location at which the resultant pressure force acts gives a moment balance static field and the location is located under the centeroid because the force increases with depth.

* There are linearly distributions for the force over the surface (from the equations).

* Errors: Un predictable fluctuations in the measured quantities, personal errors, and inaccurate reading or scaling.

References:1) Abu-Jadayil, B.Laboratory Manual for Fluid Mechanics ChE344, JUST, 2002, Irbid-Jordan.2) I. Robbert,Fluid Mechanics with Engineering Applications3rd edition, McGraw Hill, 1994.