Lab #5 Center of Pressure - Jesus Gomez

New York City College of Technology Department of Construction Management and Civil Engineering CMCE 2351 Fluid Mechanics Laboratory Laboratory Report 5: Center of Pressure Due: March 15, 2023 Submitted by: Jesus M. Gomez Group Members: Steven Angelo Camilo Rolando Cameron Angelo Abdul

Equipment 1. Hydraulic Bench 2. Quadrant Tank 3. Brass Weight 4. Beaker 5. Level 6. Thermometer Purpose To calculate the hydrostatic force exerted on a submerged plane and the theoretical hydrostatic force. Methodology One way to define the center of pressure is as follows: it is the point within a plane where the combined force exerted by a fluid can be considered to act perpendicular to that plane. The equipment allows for the direct measurement of the moment resulting from the total fluid force acting on a plane surface that is either completely or partially submerged. The quadrant tank assembly, which is used as a balance, contains water. The cylindrical sides of the quadrant have their axes aligned with the center of rotation of the tank assembly. Consequently, the combined fluid pressure acting on these surfaces does not create any moment around that center. The only moment that exists is caused by the fluid pressure acting on the plane surface, and this moment is measured through experimentation by adding weights to a weight hanger located on the opposite side of the quadrant tank. A second tank, located on the same side of the assembly as the weight hanger, enables fine adjustments to be made. A scale on the quadrant tank is utilized to determine the water level beneath the pivot. Finally, the measured moment can be compared to theoretical calculations.

Sample Calculations Fluid Name: Water Temperature, T = 22 ℃ Unit Weight ,γ = 997 kN m 3 a. Mass of brass weights, m (kg) b. Weight of brass weights, W b = mg (N) c. Solve for the location of the Center of Pressure in the horizontal direction, x , by ∑ M o . Theoretical Moment 1. Force  Distance from the free surface to centroid of plane, y c (m) y c = r 1 + r 2 2 − h  Pressure on submerged plane, P c (Pa) P c = γ y c  Area of submerged plane, A (m 2 ) A = b ( r 2 − r 1 ) = 0.075m 2  Force on submerged plane, F c (N) F c = P c A 2. Distance

 Moment of Inertia, I c I c = b ( r 2 − r 1 ) 3 12 . = 6.25*10 -6 m 4  Distance from free surface to the resultant force, y p y p = I c A y c + y c 3. Theoretical Moment, M theo (N-m) M theo = F c ( y p + h ) Actual Moment 4. Actual Moment, M actual (N-m) M actual = W b R 3 Mass of Brass weights, m (kg) Brass Weight, W b (N) Moment arm of Weights, R 3 (m) h (m) y c = r 1 + r 2 2 − h (m) P c = γ y c (Pa) F c = P c A (N) yp = Ic Ayc + yc (m) Theoretical Moment, M theo (N-m) Actual Moment, M actual (N-m) Trial 1 = 3.7 36.3 0.20 .098 0.052 510.12 3.826 0.06082564 0.635 7.26 Trial 2 = 4.7 46.1 0.20 .0785 0.0715 701.115 5.258 0.083155 0.85 9.22 Trial 3 = 5.7 55.9 0.20 .064 0.086 843.66 6.327 0.09569 1.01035 11.18 Conclusion F c y p y c b