CE321-FluidStatics - CE 321 INTRODUCTION TO FLUID MECHANICS...

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1 CE 321 INTRODUCTION TO FLUID MECHANICS Fall 2009 LABORATORY 2: FLUID STATICS OBJECTIVES To experimentally verify the accuracy of the equation derived from hydrostatic theory to predict the location of the center of pressure To determine if uncertainty in measurements appear to explain the inaccuracy in predicting the location of center of pressure using the equation derived from hydrostatic theory To comment on the apparent suitability of the equation derived from hydrostatic theory for use in engineering applications and its advantage over the experimental approach EQUIPMENT Hydrostatic pressure apparatus, set of weights, metric ruler, graduated cylinders SKETCH Figure 1. Hydrostatic Pressure Apparatus
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2 HYDROSTATIC THEORY All submerged surfaces experience a hydrostatic force. The point through which this force acts is called the center of pressure. Hydrostatic theory shows that the center of pressure of the submerged area can be calculated using Eq.1. Where y R is the distance of the center of pressure from the fluid surface y c is the location of centroid of the submerged area and I xc is the second moment of the area. c c xc R y A y I y + = (1) According to Hydrostatic Theory, the hydrostatic force (F R ) on the face of the quadrant is calculated using Eq.2. Where h c is the vertical distance from the fluid surface to the centroid of the submerged area, γ is the specific weight of the liquid and A is the submerged area. A h F c R = (2) These two general equations can be used to develop equations specific to our experiment. Consider the situation when the end face of the apparatus is partially submerged (d< l ). Eq. 2 predicts the hydrostatic force to be: w d F R 2 2 = (3) While Eq. 2 is always correct, we have only determined that Eq. 3 applies for those times in our experiment when the end face is partially submerged. It remains to be determined if this equation is suitable for situations when the end face is totally submerged. Eq. 1 predicts the center of pressure lies below the water surface a distance (y R ): d d wd wd d y R 3 2 ) 2 )( ( ) 12 ( 2 3 = + = (4) The distance y R can also be determined from the moment arm L 2 determined in the experiment: ) ( 3 2 d L L y R - - = (5)
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3 We can arrive at similar equations for the condition when the quadrant face is fully submerged. APPROACH While Eq.1 is a well established method for calculating y R , for the purpose of this experiment, you should put yourself in the position of the original investigator of this theory.
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This note was uploaded on 04/19/2010 for the course CE 321 taught by Professor Mantha,p during the Spring '08 term at Michigan State University.

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CE321-FluidStatics - CE 321 INTRODUCTION TO FLUID MECHANICS...

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