Centre Of Pressure Apparatus

ABSTRACT

The Centre of Pressure Apparatus has been designed to determine the static thrust exerted by a fluid on a submerged surface and allow comparison of the measured magnitude and position of this force with simple theory. A fabricated quadrant is mounted on a balance arm, which pivots on knife-edges. The knife-edges coincide with the centre of arc of the quadrant. Thus, of the hydrostatic forces acting on the quadrant when immersed, only the force on the rectangular end face gives rise to a moment about the knife-edges. The balance arm incorporates a balance pan for the weights supplied and an adjustable counterbalance. This assembly is mounted on top of an acrylic tank, which may be leveled by adjusting screwed feet. An indicator attached to the side of the tank shows when the balance arm is horizontal. Water is admitted to the top of the tank by a flexible tube and may be drained through a cock in the side of the tank. The water level is indicated on a scale on the side of the quadrant.

 CHAPTER ONE

1.0                                                        INTRODUCTION

1.1                                           BACKGROUND OF THE STUDY

The center of pressure is the point where the total sum of a pressure field acts on a body, causing a force to act through that point. The total force vector acting at the center of pressure is the value of the integrated vectorial pressure field. The resultant force and center of pressure location produce equivalent force and moment on the body as the original pressure field. Pressure fields occur in both static and dynamic fluid mechanics. Specification of the center of pressure, the reference point from which the center of pressure is referenced, and the associated force vector allows the moment generated about any point to be computed by a translation from the reference point to the desired new point. It is common for the center of pressure to be located on the body, but in fluid flows it is possible for the pressure field to exert a moment on the body of such magnitude that the center of pressure is located outside the body.

1.2                                                   AIM OF THE PROJECT

The main aim of this work is to setup an apparatus that is used in determining the centre of pressure and the thrust on a body immersed in a fluid basically water.

1.3                                             OBJECTIVE OF THE PROJECT

1. To determine the hydrostatic thrust acting on a plane surface immersed in water.
2. To determine the position of the line of action of the thrust and to compare the position determined by experiment with the theoretical position.

1.4                                                   SCOPE OF THE STUDY

From this experiment we are able to measure the moment due to the total fluid thrust on a wholly, or partially, submerged plane surface to be directly measured and compared with theoretical analysis. The plane area may be tilted relative to the vertical so that the general case may be studied. The water is contained in a clear Perspex quadrant, the cylindrical sides of which have their central axes coincident with the axis about which the turning moments are measured. The total fluid pressures on the secured surfaces therefore exert no moment about this pivot, the only moment being due to the fluid pressure on the plane test surface. This moment is simply measured by weights suspended from a level arm.

1.5                                              PURPOSE OF THE PROJECT

The purpose of this work is:

1. Determination of force due to hydrostatic pressure
2. Determination of Center of pressure

1.6                                           SIGNIFICANCE OF THE STUDY

1. Very efficient
2. Rigid construction

• Easy to operate

1. Long lasting

 CHAPTER TWO

2.0                                    LITERATURE REVIEW

2.1                  OVERVIEW OF HYDROSTATIC PRESSURE

The air around us at sea level presses down on us at 14.5 pounds per square inch (1 bar). We do not feel this pressure since the fluids in our body are pushing outward with the same force. But if you swim down into the ocean just a few feet and you will start to notice a change. You will start to feel an increase of pressure on your eardrums. This is because of an increase in hydrostatic pressure which is the force per unit area exerted by a liquid on an object. The deeper you go under the sea, the greater the pressure pushing on you will be. For every 33 feet (10.06 meters) you go down, the pressure increases by 14.5 psi (1 bar).

Hydrostatic pressure is the pressure that is exerted by a fluid at equilibrium at a given point within the fluid, due to the force of gravity. Hydrostatic pressure increases in proportion to depth measured from the surface because of the increasing weight of fluid exerting downward force from above.

If a fluid is within a container then the depth of an object placed in that fluid can be measured. The deeper the object is placed in the fluid, the more pressure it experiences. This is because the weight of the fluid is above it. The more dense the fluid above it, the more pressure is exerted on the object that is submerged, due to the weight of the fluid.

2.2  HISTORICAL BACKGROUND OF HYDROSTATIC PRESSURE

Some principles of hydrostatics have been known in an empirical and intuitive sense since antiquity, by the builders of boats, cisterns, aqueducts and fountains. Archimedes is credited with the discovery of Archimedes’ Principle, which relates the buoyancy force on an object that is submerged in a fluid to the weight of fluid displaced by the object. The Roman engineer Vitruvius warned readers about lead pipes bursting under hydrostatic pressure.^[2]

The concept of pressure and the way it is transmitted by fluids was formulated by the French mathematician and philosopher Blaise Pascal in 1647.

2.3                           HYDROSTATIC EXAMPLE (DAM)

Since the forces of water on a dam are hydrostatic forces, they vary linearly with depth. The total force on the dam is then the integral of the pressure multiplied by the width of the dam as a function of the depth. The center of pressure is located at the centroid of the triangular shaped pressure field 2/3 from the top of the water line. The hydrostatic force and tipping moment on the dam about some point can be computed from the total force and center of pressure location relative to the point of interest.

2.4                      HISTORICAL USAGE FOR SAILBOATS

Center of pressure is used in sailboat design to represent the position on a sail where the aerodynamic force is concentrated.

The relationship of the aerodynamic center of pressure on the sails to the hydrodynamic center of pressure (referred to as the center of lateral resistance) on the hull determines the behavior of the boat in the wind. This behavior is known as the “helm” and is either a weather helm or lee helm. A slight amount of weather helm is thought by some sailors to be a desirable situation, both from the standpoint of the “feel” of the helm, and the tendency of the boat to head slightly to windward in stronger gusts, to some extent self-feathering the sails. Other sailors disagree and prefer a neutral helm.

The fundamental cause of “helm”, be it weather or lee, is the relationship of the center of pressure of the sail plan to the center of lateral resistance of the hull. If the center of pressure is astern of the center of lateral resistance, a weather helm, the tendency of the vessel is to want to turn into the wind.

If the situation is reversed, with the center of pressure forward of the center of lateral resistance of the hull, a “lee” helm will result, which is generally considered undesirable, if not dangerous. Too much of either helm is not good, since it forces the helmsman to hold the rudder deflected to counter it, thus inducing extra drag beyond what a vessel with neutral or minimal helm would experience.^[1]

Aircraft aerodynamics

A stable configuration is desirable not only in sailing, but in aircraft design as well. Aircraft design therefore borrowed the term center of pressure. And like a sail, a rigid non-symmetrical airfoil not only produces lift, but a moment. The center of pressure of an aircraft is the point where all of the aerodynamic pressure field may be represented by a single force vector with no moment.^[2][3] A similar idea is the aerodynamic center which is the point on an airfoil where the pitching moment produced by the aerodynamic forces is constant with angle of attack.^[4][5][6]

The aerodynamic center plays an important role in analysis of the longitudinal static stability of all flying machines. It is desirable that when the pitch angle and angle of attack of an aircraft are disturbed (by, for example turbulence) that the aircraft returns to its original trimmed pitch angle and angle of attack without a pilot or autopilot changing the control surface deflection. For an aircraft to return towards its trimmed attitude, without input from a pilot or autopilot, it must have positive longitudinal static stability.^[7]

Missile aerodynamics

Missiles typically do not have a preferred plane or direction of maneuver and thus have symmetric airfoils. Since the center of pressure for symmetric airfoils is relatively constant for small angle of attack, missile engineers typically speak of the complete center of pressure of the entire vehicle for stability and control analysis. In missile analysis, the center of pressure is typically defined as the center of the additional pressure field due to a change in the angle of attack off of the trim angle of attack.^[8]

For unguided rockets the trim position is typically zero angle of attack and the center of pressure is defined to be the center of pressure of the resultant flow field on the entire vehicle resulting from a very small angle of attack (that is, the center of pressure in the limit as angle of attack goes to zero). For positive stability in missiles, the total vehicle center of pressure defined as given above must be further from the nose of the vehicle than the center of gravity. In missiles at lower angles of attack, the contributions to the center of pressure are dominated by the nose, wings, and fins. The normalized normal force coefficient derivative with respect to the angle of attack of each component multiplied by the location of the center of pressure can be used to compute a centroid representing the total center of pressure. The center of pressure of the added flow field is behind the center of gravity and the additional force “points” in the direction of the added angle of attack; this produces a moment that pushes the vehicle back to the trim position.

In guided missiles where the fins can be moved to trim the vehicles in different angles of attack, the center of pressure is the center of pressure of the flow field at that angle of attack for the undeflected fin position. This is the center of pressure of any small change in the angle of attack (as defined above). Once again for positive static stability, this definition of center of pressure requires that the center of pressure be further from the nose than the center of gravity. This ensures that any increased forces resulting from increased angle of attack results in increased restoring moment to drive the missile back to the trimmed position. In missile analysis, positive static margin implies that the complete vehicle makes a restoring moment for any angle of attack from the trim position.

2.5     REVIEW OF MOVEMENT OF CENTER OF PRESSURE FOR AERODYNAMIC FIELDS

The center of pressure on a symmetric airfoil typically lies close to 25% of the chord length behind the leading edge of the airfoil. (This is called the “quarter-chord point”.) For a symmetric airfoil, as angle of attack and lift coefficient change, the center of pressure does not move. It remains around the quarter-chord point for angles of attack below the stalling angle of attack. The role of center of pressure in the control characterization of aircraft takes a different form than in missiles.

On a cambered airfoil the center of pressure does not occupy a fixed location.^[9] For a conventionally cambered airfoil, the center of pressure lies a little behind the quarter-chord point at maximum lift coefficient (large angle of attack), but as lift coefficient reduces (angle of attack reduces) the center of pressure moves toward the rear.^[10] When the lift coefficient is zero an airfoil is generating no lift but a conventionally cambered airfoil generates a nose-down pitching moment, so the location of the center of pressure is an infinite distance behind the airfoil.

For a reflex-cambered airfoil, the center of pressure lies a little ahead of the quarter-chord point at maximum lift coefficient (large angle of attack), but as lift coefficient reduces (angle of attack reduces) the center of pressure moves forward. When the lift coefficient is zero an airfoil is generating no lift but a reflex-cambered airfoil generates a nose-up pitching moment, so the location of the center of pressure is an infinite distance ahead of the airfoil. This direction of movement of the center of pressure on a reflex-cambered airfoil has a stabilising effect.

The way the center of pressure moves as lift coefficient changes makes it difficult to use the center of pressure in the mathematical analysis of longitudinal static stability of an aircraft. For this reason, it is much simpler to use the aerodynamic center when carrying out a mathematical analysis. The aerodynamic center occupies a fixed location on an airfoil, typically close to the quarter-chord point.

The aerodynamic center is the conceptual starting point for longitudinal stability. The horizontal stabilizer contributes extra stability and this allows the center of gravity to be a small distance aft of the aerodynamic center without the aircraft reaching neutral stability. The position of the center of gravity at which the aircraft has neutral stability is called the neutral point.