Hydrostatic Force on a Submerged Surface

Hydrostatic Force on a Submerged Surface

Benson James U. Chan February 5, 2014

ABTRACT This experiment serves as a way to measure the total horizontal hydrostatic force that a liquid can exert on a plane surface by computing the moment caused by adding an appropriate counterweight to balance the experimental set-up. INTRODUCTION The purpose of this experiment is to experimentally locate the center of pressure of a vertical, submerged, plane surface. The experimental measurement is compared with a theoretical prediction. The experiment yielded results which are also similar to the theoretical values taken, with slight errors probably due to inaccuracies in measurement of values. THEORETICAL BACKGROUND The y-direction position of the center of pressure, yP, is yP = y + I . yA where I is the centriodal moment of inertia of the surface about the x-axis, and A is the surface area. The counterweight is adjusted so that the beam is horizontal when there is no water in the tank and no weight in the pan. When the tank is filled with water, the unbalanced hydrostatic force causes the beam to tilt. Adding weight W to the pan at a distance L from the pivot O exerts a moment WL that counterbalances the resultant moment due to the hydrostatic forces on the quarter-annulus-shaped body ABPQ. WL is equal to the moment due to the hydrostatic force F acting on the vertical plane surface. In this experiment the force F is not measured. Instead the theoretical value F = pghA is assumed, where h is the depth of the centroid of the surface. The moment due to F is measured and the theoretical value of F is used to compute the location of the center of pressure. Balancing the moments about O gives WL = F(H + yR) Substituting F = pghA and solving for yP yields

yP = WL

- H

pghA TEST RESULTS From the experiment, these tables were obtained: Trial 1 2 3 4 Trial

H (m) Height (m) Volume (mL) Ybar (m) Ibar (m^4) Area (m^2) measured 0.200 - H 0.142 0.058 500 0.029 1.21945E-06 0.00435 0.115 0.085 800 0.0425 3.83828E-06 0.006375 0.101 0.099 1000 0.0495 6.06437E-06 0.007425 0.083 0.117 1200 0.0585 1.00101E-05 0.008775 No. of weights measured

1 2 3 4 Yp, theo (m) Ybar + Ibar/(Ybar*A) 0.038666667 0.056666667 0.066 0.078 Yp, calculated (M/F) - H 0.080411425 0.069921412 0.078940364 0.088777389

28 39 47 58

Actual Mass (kg) Moment Force M - 0.140 AM*9.81*0.2 pgh*A 0.14 0.27468 1.2350085 0.25 0.4905 2.652478125 0.33 0.64746 3.598192125 0.44 0.86328 5.025574125 Distance (m) H + Yp 0.180666667 0.171666667 0.167 0.161 Distance (m) H + Yp 0.222411425 0.184921412 0.179940364 0.171777389

Taking the percent differences of the distances, we get a result of 23.11%, 7.72%, 7.75%, and 6.69% respectively for each of the four trials. CONCLUSION AND RECOMMENDATIONS The results that we have obtained through the experiment seem reasonable enough. Results would have been more accurate if proper measuring devices with higher precisions have been used. BIBLIOGRAPHY http://web.cecs.pdx.edu/~gerry/class/EAS361/lab/pdf/lab3_hydrostatics.pdf