Hydrostatic Pressure (Fluid Mechanics - Lesson 3)

this is the third lecture in this course on fluid mechanics today I'll be talking about hydrostatic pressure the learning objective is to understand how the pressure in the fluid relates to its depth before discussing pressure in the context of fluids let me first start by giving an example of it in the context of classical mechanics for those of you who have not yet studied classical mechanics this example will hopefully make the concept of pressure a little easier to understand so what is pressure pressure is a measure of how concentrated of forces mathematically it's represented as force divided by the surface area through which the force is acting let's look at two situations in the first a 50 kilogram weight is resting on a table in the second a 50 kilogram weight is resting on a small wooden block of negligible mass which is then resting on the table the force on the table caused by the object's weight is 50 kilograms times 9.8 meters per second squared or 490 Newtons this will be the same in both situations however in the left side example that force is distributed to the table over the relatively large surface area of the bottom surface of the weight itself and thus the pressure on the table will be relatively low well in the right hand example the force is distributed through the much smaller surface area of the block and thus the pressure on the table will be relatively high in fluent mechanics instead of one solid object imparting pressure against another solid object we have a fluid imparting pressure against a solid but the concept of a force per unit area is the same when talking about fluids there are a number of different types of pressure that one can discuss the most fundamental and important of these is something called the hydrostatic pressure this is the pressure present within the fluid when it's at rest it acts equally in all directions and it acts at a right angle to any surface that is in contact with the fluid so if we have a glass of water at a given level within the water the hydrostatic pressure which is a result of the weight of fluid above it acts on the side of the glass equally in all directions since pressure is the force divided by area if the pressure was somehow unequal it would mean the forces on the glass were unequal which would consequently result in the glass of water moving and of course we know that a glass of water at rest does not start to slide laterally on its own as another example of this imagine taking a playing card and submerging it vertically into the water the hydrostatic pressure in the water will act at a right angle to any surface in contact with the fluid that means that there is a right-sided pressure pushing on the left side of the card and a left side of pressure pushing on the right side of the card as these forces are equal the card will not spontaneously move in either direction keep in mind however that just because there is no net lateral force in the card caused by the hydrostatic pressure does not mean there is no net force of any kind on it from the last lesson we know that there is still the card's weight and the cards buoyancy so unless the card is exactly the same density as water it will still move either up or down within the water once released is there any way to quantify the hydrostatic pressure common experience might tell us that the pressure in fluid increases at increasing depth for example when you jump into a deep swimming pool if you've ever dived deep down underwater you've probably felt the pressure increasing as you go down deeper and deeper quantitatively this pressure increase can be calculated with this equation the difference in pressure between two points is equal to the density of the fluid times little G times the difference in vertical height between the two points in the case of the glass of water here if we were interested in the pressure at the bottom the two points we would use would be its bottom and top the pressure at the top is equal to atmospheric pressure and the difference in vertical height is just the depth of the water to refer back to the last lesson on Archimedes principle and buoyancy some of you might realize that the buoyant force on a submerged object which we said was equal to density of the fluid times volume of the displaced fluid times G is simply a manifestation of the difference in hydrostatic pressure that's acting upwards on the bottom side of the object and the hydrostatic pressure that's acting downwards on the top side of the object an interesting consequence of this hydrostatic pressure equation which may or may not be immediately obvious is that the pressure at any given depth is independent of the shape of the container or the path that the pressure must be transmitted along for example I could have a collection of rare and exotic jellyfish that I want to display in my home but to highlight their uniqueness maybe I want to build an equally unique aquarium system in which to house them if I wanted to know what the maximum water pressure was at the bottom of the system of tanks the only thing that would matter is the total vertical distance between the top and bottom the shape of the tanks the volume of the tanks the width and length of the connecting tubes are all irrelevant also notice that the lower tank needs a sealed lid if the lid was not there the weight of the water in the upper tank would cause the lower tank to overflow this is an example of a principle frequently paraphrased that fluids at rest seek their own level this means the surface of any fluid at rest will have the same height above the surface of the earth at all points let's look at a quantitative real world example of hydrostatic pressure we have a house at the bottom of a hill which gets its water supply from an open unpressurized water tank at the top of the hill the water tank is four meters high and full and the base of the tank is 50 meters above the level of the houses faucet given these distances what is the houses water pressure as we just reviewed the pressure difference between two points within a fluid system is the density of the fluid times G times the total difference in height between those two points so we have the water pressure in the houses faucet it's the water pressure at the very top of the tank which if the tank is open and unpressurized is equal to atmospheric pressure this equals 1,000 kilograms per cubic meter times 9.8 meters per second squared times the total height of 54 meters this is equal to five point two nine times ten to the fifth kilograms per meters second squared plus atmospheric pressure the units of kilogram per meter second squared is cumbersome to talk about so this combination has been defined as its as its own unit something called the Pascal after the French mathematician Pascal whose name has been attached to a specific physical principle that will be the subject of a future lesson in addition this idea of a pressure that is equal to some number plus atmospheric pressure gave rise to the concept of gauge pressure since atmospheric pressure is essentially equal at both the top and bottom of this type of system the gauge pressure in this type of situation is the total pressure minus atmospheric pressure when people refer to the term pressure in most everyday situations such as discussing their homes water pressure whether or not they realize it the gauge pressure is often to what they are actually referring that's an introduction to the concept of hydrostatic pressure the next lesson we'll review some of its applications in medicine you

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Keywords: hydrostatic pressure, fluid mechanics, physics, pascal, mcat

Id: C0ujLqKPWew

Length: 8min 33sec (513 seconds)

Published: Thu May 02 2013