Hydrostatic Force on a Plane Surface - Lab Report Example

Name Course Date Laboratory 1 – Hydrostatic Force on a Plane Surface Abstract The objective of this experiment is to determine the hydrostatic force acting on a plane surface when it is immersed in water and the surface if fully submerged or partially submerged. The experimental center of pressure is compared with the theoretical results for different trials. Introduction Hydrostatic force is the force acting on a flat surface of an object that is submerged in a liquid, and is given by. is the density of the liquid, g is acceleration due to gravity, h is the vertical distance between the centriod and the submerged surface, and A is the submerged surface area. The pressure exerted by the liquid at the equilibrium because of the force of gravity is called hydrostatic pressure (Biran & López-Pulido, 2014). In this experiment, hydrostatic pressure of water was determined. Method The experiment began with leveling the tank by adjusting the screwed feet until the spirit level showed that the planes were level. The counter balance jockey weight was moved until the arm was in the horizontal level. Water was then poured until the level reached the lower edge of the orange quadrant as shown below. A 50g mass was added to the balancing arm with the mass hanger. It was added with an increment of 50g until the tank was full. The balancing arm was level by adding water to the tank so as to increase the force on the plane surface. Both the height of water and the masses added were recorded. The final part of the experiment was completed by removing water through the drain valve and decrementing the mass until all the masses were removed. Results 1. Total mass Water level, d (mm) ℎ̅ (mm) yp (mm) H (mm) D (mm) F (N) M (applied) (Nm) M (hydrostatic) (Nm) h” exp (mm) h” theo (mm) 50 47 23.5 31 200 100 1.729 0.13888 0.08155 165.99 184 100 66 33 44 200 100 2.428 0.26978 0.16066 168.35 178 150 82 41 55 200 100 3.017 0.40466 0.24789 163.59 173 200 96 48 64 200 100 3.532 0.53955 0.33963 159.14 168 250 109 50 76 200 100 3.679 0.67444 0.40158 155.37 167 300 121 50 85 200 100 3.679 0.80933 0.44573 154.93 164 350 133 50 88 200 100 3.679 0.94421 0.48988 154.62 155 400 146 50 113 200 100 3.679 1.07910 0.5377 152.78 167 Sample calculations Experimental h” for partially submerged b. Free body diagram of water in the vessel c. Agraph of MApplied vs MHydrostatic The applied force and the hydrostatic force increase at a constant rate below applied force of 0.6 Nm and a different but at constant rate after. d. A graph of yp vs h” The descrepancies between the experimental and the theoritical curve is because errors made when doing the experiemnt. These included errors in measurement or during the reading of the values, for example there was parallax. On the other hand, the theoritical results are based on assumptions and this may have caused the difference. e. A graph of F vs h’ f. The resultant forces is obtained by resolving the forces on the orthogonal co-ordinate direction. The force required to maintain equilibrium on the the curved surface is equavalent to the weight of the liquid above the surface (Munson, Young, & Okiishi, 2002). g. Hydrostatic forces are applied in various applications. It can be applied in dams, submarines, aquariums and boats. The knowledge of hydrostatic forces can be used in determination of hydrostatic forces against a dam or vertical wall in a fluid, the design of dams and boats (Post, 2011). h. In the experiment, the forces applied on the vertical direction of the submerged object counteract the mass applied on the arm. It shows that as we move away form the sea level, the pressure change due to the change in the amount of liquid above. The water pressure was high such that the 450g mass was supported in static equilibrium. The curved surface enables a boat to have a large surface through which the water can act on the vessel to enable less change in depth. Conclusion The forces acting vertically on the bottom and top of the surface of the material create a buoyancy force, F. The weight of the material balances the bouyancy force. The centroid of the submerged material is the center of that bouyancy. The experimental force and the theoritical forces are nearly identical as it is shown in the graph. References Lab 2: Metacentric height Summary The objective of this experiment was to determine the metacentric height of an object. The experimental results that were obtained were compared with the results obtained from the experimental models. Introduction The stability of a floating object on water such a ship is important. The ability of the object or a vessel to remain upright is determined by the relation locations of the metacentre, M and the center of gravity, G. Metacentric height, GM, is the distance between the two. The object is stable if the metacentre is located above the centre of gravity. But if it is located below the centre of gravity, the system is not stable as the overturning moment is induced (Biran & López-Pulido, 2014). Neutral equilibrium position occurs if the metacentre is at the same level as the centre of gravity. The weight of the material acts downwards through the centre of gravity, G as shown below. B is the centre of buoyancy and M is the metacentre Method This began with weighing the weight used to traverse across the platoon width for induced tilt. The weight of an assembly of platoon, mast and two weights were also determined. The sliding weight was then positioned on the mast to locate the centre of gravity for the assembly. The location of the centre of gravity was determined using a tight string around the mast, and allow the assembly to be suspended from it, and changing the position of the suspension until the mast was horizontal. The distance, y, which is the COG height is the distance between the pivot and the base of the platoon. The inclining weight was moved to the centre of platoon at the 0 mm point on the linear scale before tightening the screw. The inclining weight was then transverse to the right in 10 mm increments and the angular displacement of the plump line was measured. This was repeated six times until the end of the scale has been reached. Steps 6 -7 were repeated for the left hand direction. Finally, the location of the platoon centre of gravity was changed by moving the sliding weight up the mast up to the midway and steps 5 to 8 were repeated. The table of the results obtained from the experiment Plantoon length (m) Plantoon width (m) Total weight (Kg) Inclining weight (Kg) Centre of gravity height (m) Depth of immersion (m) Theoretical GM (m) Position of inclining weight (m) Angle of heels Experimental GM (m) 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 0 0 0 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 10 1.4 0.93985 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 20 2.6 1.012146 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 30 4.2 0.93985 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 40 5.4 0.974659 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 50 6.9 0.953471 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 60 8.2 0.962773 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 70 9.3 0.990379 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 80 10.5 1.002506 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 -10 1.5 -0.87719 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 -20 2.7 -0.97466 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 -30 4.6 -0.85812 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 -40 5.5 -0.95694 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 -50 6.9 -0.95347 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 -60 8.5 -0.92879 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 -70 9.7 -0.94954 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 -80 10.9 -0.96572 Sample of calculations V = 0.35 x 0.2 x 0.2 = 0.0014 m3 BM = OB = 0.5 x 0.2= 0.1 GM = BM + OB – OG = 0.16667 + 0.1 - 0.09 = 0 Experimental A graph of CoG verses metacentric height The change in the location of the centre of gravity does no dictate the metacentric position,but it is determined by the shape of section under water (Derrett & Barrass, 2006). The decrepancies between the experimental and the theoritical results was due to errors made in the experiment. Errors were made when reading the weight of the materials, but it was very small with a value less than 10%. Some errors were made when reading the values of height. This is due paralax and assumptions. the overall error was very small as the results of the theoritical model is almost similar to the experimental values. Applications Building water tanks that are sitting on a very high place like a tank on top of a mountain used for drinking. It is also used in hospitals where a patient has a catheter and the catheter is placed at a high place so that the hydrostatic pressure ciould push the liquid and nutrients to the bloodstreams. The knowlegde here is used in the construction of ships (Granger, 2012). References Biran, A., & López-Pulido, R. (2014). Ship hydrostatics and stability. Derrett, D. R., & Barrass, C. B. (2006). Ship stability for masters and mates. Burlington, Mass: Butterworth-Heinemann. Granger, R. A. (2012). Fluid Mechanics. Dover Publications. Read More

The water pressure was high such that the 450g mass was supported in static equilibrium. The curved surface enables a boat to have a large surface through which the water can act on the vessel to enable less change in depth. Conclusion The forces acting vertically on the bottom and top of the surface of the material create a buoyancy force, F. The weight of the material balances the bouyancy force. The centroid of the submerged material is the center of that bouyancy. The experimental force and the theoritical forces are nearly identical as it is shown in the graph.

References Lab 2: Metacentric height Summary The objective of this experiment was to determine the metacentric height of an object. The experimental results that were obtained were compared with the results obtained from the experimental models. Introduction The stability of a floating object on water such a ship is important. The ability of the object or a vessel to remain upright is determined by the relation locations of the metacentre, M and the center of gravity, G. Metacentric height, GM, is the distance between the two.

The object is stable if the metacentre is located above the centre of gravity. But if it is located below the centre of gravity, the system is not stable as the overturning moment is induced (Biran & López-Pulido, 2014). Neutral equilibrium position occurs if the metacentre is at the same level as the centre of gravity. The weight of the material acts downwards through the centre of gravity, G as shown below. B is the centre of buoyancy and M is the metacentre Method This began with weighing the weight used to traverse across the platoon width for induced tilt.

The weight of an assembly of platoon, mast and two weights were also determined. The sliding weight was then positioned on the mast to locate the centre of gravity for the assembly. The location of the centre of gravity was determined using a tight string around the mast, and allow the assembly to be suspended from it, and changing the position of the suspension until the mast was horizontal. The distance, y, which is the COG height is the distance between the pivot and the base of the platoon.

The inclining weight was moved to the centre of platoon at the 0 mm point on the linear scale before tightening the screw. The inclining weight was then transverse to the right in 10 mm increments and the angular displacement of the plump line was measured. This was repeated six times until the end of the scale has been reached. Steps 6 -7 were repeated for the left hand direction. Finally, the location of the platoon centre of gravity was changed by moving the sliding weight up the mast up to the midway and steps 5 to 8 were repeated.

The table of the results obtained from the experiment Plantoon length (m) Plantoon width (m) Total weight (Kg) Inclining weight (Kg) Centre of gravity height (m) Depth of immersion (m) Theoretical GM (m) Position of inclining weight (m) Angle of heels Experimental GM (m) 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 0 0 0 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 10 1.4 0.93985 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 20 2.6 1.012146 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 30 4.2 0.93985 0.35 0.2 1.52 0.2 0.09 0.02 0.

0866667 40 5.4 0.974659 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 50 6.9 0.953471 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 60 8.2 0.962773 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 70 9.3 0.990379 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 80 10.5 1.002506 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 -10 1.5 -0.87719 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 -20 2.7 -0.97466 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 -30 4.6 -0.85812 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 -40 5.5 -0.95694 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 -50 6.9 -0.95347 0.35 0.2 1.52 0.2 0.09 0.02 0.

0866667 -60 8.5 -0.92879 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 -70 9.7 -0.94954 0.35 0.2 1.52 0.2 0.09 0.02 0.0866667 -80 10.9 -0.96572 Sample of calculations V = 0.35 x 0.2 x 0.2 = 0.0014 m3 BM = OB = 0.5 x 0.2= 0.1 GM = BM + OB – OG = 0.16667 + 0.1 - 0.

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