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7.5 Fluid Pressure and Forces

Calculate forces on a wading pool plate and aquarium face; understand density-depth-area relationship; learn Normal Distribution and Probability Density Function.

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7.5 Fluid Pressure and Forces

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  1. Photo by Vickie Kelly, 2006 Greg Kelly, Hanford High School, Richland, Washington 7.5 Fluid Pressure and Forces Georgia Aquarium, Atlanta

  2. What is the force on the bottom of the aquarium? 2 ft 3 ft 1 ft

  3. All the other water in the pool doesn’t affect the answer! If we had a 1 ft x 3 ft plate on the bottom of a 2 ft deep wading pool, the force on the plate is equal to the weight of the water above the plate. density depth area pressure

  4. It is just a coincidence that this matches the first answer! 0 2 ft 2 3 ft What is the force on the front face of the aquarium? 2 ft Depth (and pressure) are not constant. If we consider a very thin horizontal strip, the depth doesn’t change much, and neither does the pressure. 3 ft 1 ft depth density area

  5. We could have put the origin at the surface, but the math was easier this way. A flat plate is submerged vertically as shown. (It is a window in the shark pool at the city aquarium.) 2 ft Find the force on one side of the plate. 3 ft Depth of strip: Length of strip: Area of strip: 6 ft density depth area

  6. Examples: The mean (or ) is in the middle of the curve. The shape of the curve is determined by the standard deviation . mu x-bar sigma Normal Distribution: For many real-life events, a frequency distribution plot appears in the shape of a “normal curve”. 13.5% 34% 2.35% heights of 18 yr. old men 68% standardized test scores 95% lengths of pregnancies 99.7% time for corn to pop “68, 95, 99.7 rule”

  7. Normal Probability Density Function: (Gaussian curve) Normal Distribution: The area under the curve from a to b represents the probability of an event occurring within that range. 13.5% 34% 2.35% “68, 95, 99.7 rule” In Algebra 2 we used z-scores and a table of values to determine probabilities. If we know the equation of the curve we can use calculus (and our calculator) to determine probabilities:

  8. Normal Probability Density Function: (Gaussian curve) Normal Distribution: The good news is that you do not have to memorize this equation! Example 6 on page 406 shows how you could integrate this function to predict probabilities. In real life, statisticians rarely see this function. They use computer programs or graphing calculators with statistics software to draw the curve or predict the probabilities. p

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