Wednesday, July 25, 2012

The Mountains of West Virginia and Pascal's Principle

Some of the most memorable experiences of our trip were the breathtaking views at higher elevations.  We visited Bald Knob and Gaudineer Knob; both views were something to behold with respective elevations of roughly 4800 feet and 4430 feet above see level.  These views were remarkable, and the physics we can derive from them is paramount to developing a better understanding of fluid mechanics.  Specifically, we will entertain Pascal's Principle.
Pascal's Principle is usually stated as the pressure in a fluid is transmitted undiminished throughout the fluid.  Yet, this also tells us that the height or depth within the fluid also determines the absolute pressure exerted.  Quantitatively, this is written as P = «P» + pgh:  Pressure is equal to atmospheric pressure plus density of the fluid times gravity times height.  This height element is why our ears "pop" when ascending or descending heights quickly.  Our bodies are attmepting to equalize the pressure inside our body with the surroundings.  The trip up to Bald Knob was on a Shay Locomotive and took close to an hour and a half for a distance of eleven miles.  This rate of ascension was gradual and did not cause my ears to "pop, as they did when driving up to Cathedral State Park.
Here are a couple of questions to consider, each having its answer within the noted equation above:
1.  Why are there fewer air molecules with an increase in height?
2.  From the equation, why would "going down" equate to an increase in pressure?





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