To experimentally determine the centre of pressure on fully and partially submerged vertical plane surfaces and to compare that with the theoretical center of pressure. 2. Theory A fabricated quadrant is mounted on a balance arm which pivots on knife edges. The line of contact of the knife edges coincides with the axis of the quadrant. Thus, of the hydrostatic forces acting on the quadrant when immersed, only the force on the rectangular face end gives rise to a moment about the knife edge axis. Figure 1 – Hydrostatic pressure apparatus
Hydrostatic pressure force on partially submerged vertical plane surface Figure 2 – Hydrostatic pressure force on partially submerged vertical plane surface C – Centre of gravity P – Centre of pressure D – Quadrant height B- Quadrant breadth H – Base of quadrant to pivot height d – base of quadrant to free surface height h- – Centered to free surface height Hal – Centre of pressure to free surface height h2o – Centre of pressure to pivot height L – Distance from pivot to weight hanger W – Applied weight at the hanger By balancing moments about the pivot, an experimental value for the h2o can be obtained as follows.
Also the theoretical value of h2o can be obtained using the parallel axis theorem. Hydrostatic pressure force on fully submerged vertical plane surface Figure 3 – Hydrostatic pressure force on fully submerged vertical plane surface D – Quadrant height Hal – Centre of pressure to free surface height As done in the previous section, by balancing moments, the experimental value of h2o can be obtained. Also the theoretical value can be obtained using the 3. Methodology 1. Position the balance arm on the knife edge and locate the weight hanger in the rove at the end of the balance arm.
Then make the balance arm horizontal by moving the counter balance weight. 2. Add a small weight to the weight hanger. 3. Smoothly add water until the hydrostatic thrust on the vertical plane of the quadrant brings the balance arm back to horizontal position. 4. Read the depth of immersion, d from the scale on the apparatus. 5. Repeat step 2, 3, 4 for another 5-6 weight increments. 6. Repeat the experiment for the used weight increments while unloading by draining out water.