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Lab #2 – Hydrostatic Pressure ENGR 341 – Fluid Mechanics September 27/28, 2007 In this lab, you will apply the principles of hydrostatics for two separate experiments. Part 1 – Hydrostatic Force Using the Hydrostatic Pressure Apparatus (shown in the figure above) with the Armfield Hydraulics Bench, you will determine the hydrostatic force on the submerged plane surface. You will also determine the location of this force and compare it to the theoretically-derived location. Procedure: Place the empty tank on the Bench and position the balance arm on the pivot. Place the balance pan in the groove at the end of the balance arm. Level the tank. Position the counterbalance weight until the balance arm is horizontal. Add a known amount of weight to the balance pan. Pour water into the tank until the balance arm is horizontal again. (Note: it may be easier to overfill then use the drain to level it.) When the arm is level, this means that the force on the vertical face of the quadrant balances out the force due to the added weight. Read the depth of immersion from the scale on the face of the quadrant. Repeat the experiment by adding more weights (increments of 50g should work fine) until you have at least two measurements in which the vertical face is completely submerged. Calculate the magnitudes and locations of the forces for each weight combination. Compare these locations with the theoretical positions. Pre-determined Dimensions: Width of Quadrant B=0.075m Height of Quadrant D=0.100m Length of Balance L=0.275m Quadrant to Pivot H=0.200m For Partially Submerged Surfaces: d = depth of submersion F = hydrostatic force h = depth to the centroid h’ = depth to the center of pressure h” = distance to the line of action of thrust below the pivot Partially Submerged Equations: Bd 2 Hydrostatic Force: F = γ 2 mgL Experimental Location of Force: h" = F d Theoretical Location of Force: h" = H − 3 For Fully Submerged Surfaces: Fully Submerged Equations: ⎛ D⎞ Hydrostatic Force: F = γBD⎜ d − ⎟ ⎝ 2⎠ mL Experimental Location of Force: h" = ⎛ D⎞ ρBD⎜ d − ⎟ ⎝ 2⎠ 2 D2 ⎛ D⎞ + ⎜d − ⎟ 12 ⎝ 2⎠ Theoretical Location of Force: h" = +H −d D d− 2 Questions to Answer in Report: 1. Describe the variation of the hydrostatic force with depth. 2. Describe the relationship between the depth of the center of pressure and the depth of immersion. 3. For both (1) and (2), describe the same when the vertical face becomes completely submerged. 4. Explain any discrepancies between the experimental and theoretical results. Results Table: mass (m) submergence (d) force (F) h” experimental h” theory grams meters Newtons meters meters Part 2 – Buoyancy For this part of the lab, you must determine the specific gravity of three cylinders (plastic, concrete, and steel). Use the scale system provided and your knowledge of Buoyant Forces. Show all appropriate equations used to calculate your answers and include an appropriate Free Body Diagram.
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