Hydrostatic Pressure: a) In the Hydrostatic Pressure experiment, how does hydrostatic force vary on the quadrant as water and weight are added? b) What happens to center of pressure as water is added to the tank? Calculate the hydrostatic force, theoretical depth of center of pressure, experimental depth of center of pressure given the following: Height of quadrant (D) = 0.1 m Width of quadrant (B) = 0.075 m Length of balance arm (L) = 0.275 m Quadrant to pivot distance (H) = 0.2 m Mass (m) 0.05 kg Depth of immersion (d) = 0.046 m Density of water (p) = 1000 kg/m³ m.g 9. B D
a) How does hydrostatic force vary on the quadrant as water and weight are added
In a hydrostatic pressure experiment, the hydrostatic pressure increases with the increase in depth or height of the fluid column above a given point. This pressure is caused by the weight of the fluid above that point and is known as hydrostatic pressure.
In the pressure experiment there is a quadrant which is located on a balance arm that rests on knife edge. Its is located in such a position that the the edge of the knife coincides with the center of arc of the quadrant. Thus the hydrostatic force acting on any point of the curved surfaces is perpendicular to the surface and passes through the pivot point, which is located at the origin of the radii. As a result, the hydrostatic forces on the upper and lower curved surfaces do not produce any net effect, and thus do not cause any torque that could disturb the assembly's equilibrium. Similarly, the horizontal forces acting on the sides of the quadrant are balanced and cancel each other out.
This in turn will creates a situation that hydrostatic force which acts on the vertical surface of the quadrant only creates a moment about the pivot point. To balance the hydrostatic force on the vertical submerged face, a counteracting balance weight is used. Therefore, the resultant hydrostatic force on the face can be determined by considering the value of the balance weight and the depth of the water.
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