Then, calculated hydrostatic force and center of pressure on the vertical face of the quadrant can be compared with the experimental results.Ī YouTube element has been excluded from this version of the text. Y : distance between the pivot and the center of pressure (Figure 1.2). L : length of the balance arm (Figure 1.2)
The system is in equilibrium if the moments generated about the pivot points by the hydrostatic force and added weight (=mg) are equal, i.e.:.The resultant hydrostatic force on the face can, therefore, be calculated from the value of the balance weight and the depth of the water. The hydrostatic force on the vertical submerged face is counteracted by the balance weight.The forces on the sides of the quadrant are horizontal and cancel each other out (equal and opposite).Hydrostatic forces on the upper and lower curved surfaces, therefore, have no net effect – no torque to affect the equilibrium of the assembly because the forces pass through the pivot. The hydrostatic force at any point on the curved surfaces is normal to the surface and resolves through the pivot point because it is located at the origin of the radii.In this experiment, when the quadrant is immersed by adding water to the tank, the hydrostatic force applied to the vertical surface of the quadrant can be determined by considering the following :
The water level is indicated on a scale on the side of the quadrant.
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 hydrostatic force and its line of action (center of pressure) can be determined for different water depths, with the quadrant’s vertical face either partially or fully submerged.Ī level indicator attached to the side of the tank shows when the balance arm is horizontal. Since the line of actions of hydrostatic forces applied on the curved surfaces passes through the pivot point, the forces have no effect on the moment. This moment can be counterbalanced by adding weight to the weight hanger, which is located at the left end of the balance arm, at a fixed distance from the pivot.
The knife edges coincide with the center of the arc of the quadrant therefore, the only hydrostatic force acting on the vertical surface of the quadrant creates moment about the pivot point. The quadrant is mounted on a balance arm that pivots on knife edges. The water tank has a drain valve at one end and three adjustable screwed-in feet on its base for leveling the apparatus. The equipment is comprised of a rectangular transparent water tank, a fabricated quadrant, a balance arm, an adjustable counter-balance weight, and a water-level measuring device (Figure 1.1).
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