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Hydrostatic Pressure Lab

Hydrostatic Pressure Lab - Introduction As stated in the...

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Introduction As stated in the “Hydrostatic Pressure” lab procedure 1 , the objective of the lab is to determine the magnitude of a hydrostatic force on a plane surface and the location of this force. By associating height of water, a balance pan, and a counterweight with the Hydrostatic Pressure Apparatus this will be achieved. Furthermore, these values will be determined by experimentation and corresponding equations. Determination of hydrostatic forces is applicable to bodies submerged in a fluid. As stated in Fundamentals of Fluid Mechanics 2 , These forces develop on the surface of the body and are a result of the fluid itself. Hydrostatic forces are dependent upon the specific weight of the fluid, the total area, and depth of the centroid of the body which is reflected in the equation. Knowledge of the magnitude and location of such forces is crucial to the design of bodies such as ships, dams and similar hydraulic systems. The location of the hydrostatic force is found by determining the coordinates which together are referred to as the center of pressure. The greater the depth of submergence of the body in the fluid, the closer the center of pressure is to the resultant hydrostatic force. Hydrostatic pressure is a major factor considered by design engineers when determining the safety and effectiveness of submerged body applications. Relevant Theory When considering a column of fluid with a given depth, the fluid particles at the upper surface of the column are only subject to atmospheric pressure. The particles below the surface, at a given depth H, however are subject to an increasing pressure build up. An incompressible fluid is a fluid with a constant density. In regards to this experiment treating the fluid used as incompressible is a good assumption being that the only fluid was water originating from the one source, the faucet. When there is an incompressible column of fluid not subject to shearing stresses the relationship between pressure and depth is linear. This relationship can be described by Equation 1. 1
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P =γ× H + P 0 (1) P = Pressure at Depth H γ = Specific Weight of fluid P 0 = Pressure at surface According to Pascal’s law; the pressure at a point in a fluid at rest, or in motion, is independent of direction as long as there are no shearing stresses present. This means that an object fully submerged in a fluid is subject to pressure forces from all directions on every face of the object. Pascal’s law applies to this experiment. When an object is partially or fully submerged, in a fluid, the hydrostatic pressure acts on all faces of the object submerged in the fluid. As previously mentioned, if this fluid is incompressible and not subjected to shearing stresses, the pressure will vary linearly with depth.
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