Hydrostatic Pressure - Lab Report Example

Hydrostatic Pressure – Lab Report By Institute The pressure exerted by liquids at equilibrium under effect of gravity is of immense practical importance. A lab practical was undertaken to study and understand the principles, working and utility of this fluid pressure. This lab report includes the theoretical background, method used in lab, results obtained therein, discussion regarding errors and possible improvements and conclusion regarding the utility of Hydrostatic pressure in general and experimental procedure followed in particular. Keywords: Hydrostatic pressure Hydrostatic Pressure – Lab Report Introduction: Hydrostatic pressure is “the pressure exerted by a fluid at equilibrium due to the force of gravity” (Myers, 2006). A fluid in this condition is known as a hydrostatic fluid (Myers, 2006). So our Hydrostatic pressure lab was to determine the hydrostatic pressure of water on a flat surface, adding weight and then filling the tank with water to the point where the apparatus was in equilibrium in order to calculate the force on the flat surface using the given equations. The Fluid Mechanics laboratory provides a “hands on” environment that is crucial for developing students understanding of theoretical concepts (Damodara Reddy, 2012). Fluid mechanics laboratory is where fluids and their flows are studied and observed such as “Pressure variations of compressible fluids when they are allowed to flow through convergent divergent nozzles, calibration of pressure gauges and theoretical demonstration of different laws of fluid mechanics and others” (Desmukh, 2009). Objective: The objective of this experiment was to “calculate the hydrostatic force a fluid exerts on a submerged plane surface” and then liken the experimental hydrostatic force to the theoretical hydrostatic force. Furthermore, we will calculate the center of pressure for a plane surface partially submerged in a fluid and then for the plane surface full submerged in the fluid. Methodology: Firstly, the following measurements were made; of quadrant’s end face, lever arm length and the distance between pivot and the lower edge. Now with the apparatus placed steadily on the stall, position the balance arm on the knife edge pivot and hang the weight pan from the balance arm.The apparatus was made use of adjustable feet and spirit level. Now the counterbalance was rotated until the balance is level and the counterbalance was to remain at the same position for the whole experiment.Now a mass of 50g was positioned on the weight pan and water was added until the balance arm was horizontal. The mass on the water pan and water level were measured Now we increment the mass by 50g until the total mass is 450g and the water level is an inch above the top edge of the vertical face, and measure the mass on the pan and water level after every increment.Then to calculate the density of the fluid we record the temperature and compare the value to the table in appendix 2 to find the corresponding density. Now we remove the masses from the weight pan in 50g increments and after each removal we drain water from the container until the balance arm is horizontal. Now again, we record the mass remaining on the pan and the associated water level at each step until all masses have been removed. Now we calculate XcpT by using equations: For the plane partially submerged: For the plane fully submerged: After that we calculate XcpA from the moment balance in each case through the use of: Figures: Hydrostatic Pressure Schematic when the plane surface is partially submerged: Hydrostatic Pressure Schematic when the plane surface is fully submerged: Results and observations: Table 1. Dimenstions fo the Apparatus End face length, d 100 End face breadth, b 75 Level arm, L 275 Bottom edge below pivot, X 200 Water temperature 25.3C Water Density 997.05 kg/m3 Source: Appendix II Theoretical and experimental distances from the pivot to the centre of pressure No. Mass, m (kg) Water depth, h (m) Location of Centroid, (m) Submerged area, A (m3) Secodn moment of arean I, (m4) Hydrostatic Force, F (N) Experimental Location of cp, XcpA (m) Theoretical location of XcpT, (m) loading unloading average 1 0 0 0 0 0 0 2 0.05 0.046 0.046 0.0460 0.0230 0.00345 6.08E-07 0.776 0.1738 0.1847 3 0.10 0.065 0.065 0.0650 0.0325 0.004875 1.70E-06 1.550 0.1740 0.1783 4 0.15 0.081 0.081 0.0810 0.0405 0.006075 3.30E-06 2.416 0.1675 0.1730 5 0.20 0.094 0.094 0.0940 0.0470 0.00705 5.19E-06 3.260 0.1655 0.1687 6 0.25 0.104 0.108 0.1075 0.0575 0.0075 6.25E-06 4.220 0.1598 0.1645 7 0.30 0.119 0.119 0.1190 0.0690 0.0075 6.25E-06 5.060 0.1599 0.1621 8 0.35 0.131 0.131 0.1310 0.0810 0.0075 6.25E-06 5.940 0.1590 0.1603 9 0.40 0.144 0.144 0.1440 0.0940 0.0075 6.25E-06 6.900 0.1564 0.1589 10 0.45 0.154 0.154 0.1540 0.1040 0.0075 6.25E-06 7.630 0.1591 0.1580 Discussion: The most common error is the error of the human eye, that is, the measurements and readings are all effected by the reflex timing and sharpness of the eye of the person who is responsible for recording all the values (Desmarais, 2000). Other errors include the error in the apparatus, if the markings of the ruler or if the weighing machine and other instruments used for various measurements are not properly calibrated then the faulty measurements will be recorded which will affect the overall values and ultimately result in a faulty graph (Damodara Reddy, 2012). Furthermore, if the counterbalance was disturbed even for a bit during the whole experiment after the initial calibration then again the measurements and the graphs will be incorrect and faulty (Desmarais, 2000). Another limitation was that when the weight of 50g was added the water level was also to be maintained and the water being added was to be added very slowly and special care was to be taken that no water was spilled onto the top of the plate support system. Conclusion: The graph and the angle show that the experiment conducted and whose results are provided was accurate. The angle could not be 45 degrees since we did not have ideal conditions, but is very close to 45. This demonstrates that the experiment conducted was very accurate and that XcpT and XcpA are very close to one another. References Damodara Reddy, A. (2012). Fluid Mechanics and Hydraulic Machines Lab Manual. Saarbrücken: LAP LAMBERT Academic Publishing. Desmarais, N. (2000). Fluid Mechanics: an interactive text200019James A. Liggett; David A. Caughey. Fluid Mechanics: an interactive text . http://www.pubs.asce.org: ASCE Press July 4, 1998. $100.00; $75.00 students and ASCE members. Electronic Resources Review, 4(3), pp.19-20. Desmukh, T. (2009). Fluid mechanics and hydraulic machines. [S.l.]: Laxmi Publications. Myers, R. (2006). The basics of physics. Westport, Conn.: Greenwood Press. Read More