hi everyone today we're going over chapter four of physics for the mcat which covers fluids chapter 4.1 is about the characteristics of fluids and fluids can be either a gas or liquid because a fluid is anything that has the capability to flow and gases and liquids are both able to flow fluids are weak to shear forces which are also known as tangential forces and this is any force that is tangent to an object so for example if you were to run your hand across the surface of your desk your the material of your desk wouldn't move anywhere and this is because your desk is solid and therefore it's strong to sheer forces but if you were to run your hand across the surface of a pool of water this water would ripple and it would distort because it's weak to sheer forces the density of any material is rho which is the symbol here and this is equal to mass over volume in si units this is in kilograms per meter cubed but generally you'll see density in units of grams per centimeter cubed the weight of an object is equal to the force of gravity and this is equal to rho times volume times the gravitational acceleration and this is true because the weight of an object is mass times the gravitational acceleration and since mass equals rho times volume according to this equation here the weight of a liquid is equal to the density times the volume times the gravitational acceleration the specific gravity of an object is when you compare the density to the density of water so the specific gravity of anything is rho which is its density divided by one gram per centimeter cubed which is the density of water the pressure on an object is equal to the amount of force on it over area and this is in units of pascals this conversion is important to remember because sometimes on the mcat you're given a problem in terms of pascals or in terms of millimeters of mercury or tor and you need to convert it to atm in order to do any calculations with it so make sure to memorize this conversion here and so the absolute pressure of an object is how much pressure is exerted on it at any given moment the atmospheric pressure is how much pressure is exerted on it when it's in the air and atmospheric pressure changes with altitude so as you go higher in altitude there's less atmospheric pressure because there's less air weighing down on the object the hydrostatic pressure of an object is how much pressure is on it when it is in a body of water or another fl or another fluid and this pressure is equal to p naught which is the atmospheric pressure on the surface of the water generally this is one atm which is equal to 760 torr which is by definition equal to 760 millimeters of mercury and it's equal to 1.013 times 10 to the fifth pascals and this has to be added to the pressure that the water exerts and so the pressure the water exerts is rho which is the the density of the fluid times g which is the gravitational acceleration times z which is the depth sometimes you'll see this equation as the pressure equals p naught plus rho g h where h is the height or the distance that the object is beneath the surface of the water and what this means is that the further down into a body of water you are the more pressure there is because the more fluid there is above the object to exert pressure on it gauge pressure is another measure of pressure and basically the gauge pressure is all of the pressure except for the atmospheric pressure and so the equation for gage pressure is just the absolute pressure minus the pressure of the atmosphere and this is a different equation to remember it by but what i usually remember by is that the gage pressure is just the absolute pressure minus one atm or whatever the atmospheric pressure is usually it's one atm because the pressure at sea level is defined as one atm chapter 4.2 is about hydrostatics and it starts off with the idea of pascal's principle which is the idea that if you apply a certain force to an incompressible fluid such as a liquid to a certain area of this fluid you'll generate a certain amount of pressure and this pressure will be applied to a different area of the fluid um with a different amount of force so this idea is helpful in the context of a hydraulic system so in this hydraulic system we have one opening with an area of one meter squared and another opening with an area of 10 meters squared so if there was a very very large heavy block on one end a block that you couldn't lift yourself but instead you could apply a pressure or a force onto the other smaller side so if you were to apply 10 newtons of force onto the smaller side divided by the area of one meter squared this would cause a pressure of 10 pascals and to find out the force applied to the large block we can write that 10 pascals equals the amount of force over 10 meters squared and so you can see that the force here is equal to a hundred newtons so this generates a mechanical advantage so you only applied 10 newtons of force over on the left but you got out 100 newtons of force however note that the amount of distance that you push the fluid down on the side is not the same amount of distance that the block will rise on the other side and this is because if you imagine pushing some water and meter down a very skinny tube this is not the same amount of water that will rise in a very wide tube and to figure this stuff out we'll have to use the concept of work so first in order to figure out the volume that is pushed up and down on either side we use this equation which is volume equals area times distance which is pretty intuitive because if you have any sort of box um the volume of it is the area times the height and this is also intuitive because volume is in meters cubed and area is in meters squared and distance is in meters and so the volume displaced on one side is equivalent to the volume displaced on the other side so these two terms are equal so if we displaced one meter squared of area times a distance of one meter this is equal to one meter cubed and so on the other side we have still one meter cubed equals 10 meters squared area and so we know the distance has to be 0.1 meters so although you had a mechanical advantage you only inputted 10 newtons but you got 100 newtons out you only got one tenth of the distance that you pushed it so this is related to the idea of work because we know that the idea of work is work equals force times distance um and we learned in the last episode that this work is also equal to pressure times the change in volume and so we learned from pascal's principle um that pressure is equal to force over area and we learn from the second equation that volume is equal to area times distance and so pressure times change in volume can also be written this way and we also know that this is equal to the same thing but on the right side and so we can use this to understand that the work done on either side is the same the next concept is archimedes as principle which is the idea that if you had a body of fluid and you were to put an object in it then the amount of fluid that would be displaced is related to the object's density and the object's volume which means it's related to the object's mass and in fact the mass of the object is the exact mass of fluid that it would displace so this equation sums this concept up it says that the buoyant force of an object so if an object is floating the buoyant force is equal to the gravitational force because the gravitational force is the force pulling it down and if the object is floating that means it's at equilibrium it's not moving up or down and so the gravitational force pulling it down should be equal to the buoyant force from the fluid pushing it up and this buoyant force is equal to the density of the fluid times the volume of fluid displaced times the gravitational acceleration which is also equal to the density of the fluid times the volume of the object that has been submerged times the gravitational constant from this you can see that the volume of fluid that is displaced is equal to the volume of the object that was submerged which makes sense because if you imagine that you had a cup of water that was completely full and then you dropped some very heavy objects into it then the amount of water that would overflow over the top of the cup would be equal to the volume of the objects that you put into it if on the other hand you had an object that was maybe 10 the density of water then only 10 of this object would sink below the surface of the water and we can use these previous equations to figure out why so if this object was 10 the density of water it would be 0.1 grams per centimeter cubed so if this object was also one centimeter cubed then this object would be 0.1 grams so zero if this object were 0.1 grams then it would only be able to displace 0.1 grams of water and if it were we're only able to displace 0.1 grams of water which has a density of 1 centimeter cubed then this would be 0.1 centimeters cubed of water so of this one centimeter cubed object it would only sink 0.1 centimeters cubed the molecular forces of a liquid also affect the way that it behaves so if a liquid was shown to have very high surface tension which means it has this convex sort of shape this means that it has very high cohesion which means that the different molecules of the liquid like to stick to other molecules of the liquid if it were to form this concave meniscus it means that it has high adhesive forces which means that the molecules of the liquid like to stick to the molecules of the container chapter 4.3 is about fluid dynamics viscosity is denoted by the greek letter eta which kind of looks like an n and it's in units of pascal seconds or this viscosity is the resistance to flow so a higher viscosity would mean a higher viscous drag which means the liquid doesn't like to flow so you can think of honey which is very viscous which doesn't like to flow or water which isn't very viscous which flows so an ideal fluid is a fluid that has no viscosity this ideal fluid doesn't necessarily exist in real life but it's very useful to create models in physics and a fluid with no viscosity is called inviscid there are two types of flow and these are called laminar and turbulent flow laminar flow is orderly and predictable so in this image you can see that the lines are fairly orderly and predictable the other kind of flow is called turbulent flow and turbulent flow is flow that is very disorderly and chaotic and it's unpredictable it's very hard to find mathematical models to describe turbulent flow but what you need to know about turbulent flow is that when it happens it's because of the fluid is moving at too high of a velocity to remain laminar and also that the lines of fluid most adjacent to the edges remain in a laminar fashion the flow rate of any liquid can be calculated with this equation it's called poissell's law i think that's how it's pronounced and so q which is the flow rate is equal to pi r which is the radius of the pipe to the fourth power times delta p which is the change in pressure from the beginning of the pipe to the end of the pipe divided by 8 eta times l which is the length of the pipe so this equation seems very complicated but i wouldn't recommend memorizing it what i would recommend knowing is that the radius is to the fourth power which means that if the radius were increased by even a little bit this would cause a huge increase in the flow rate and if the radius was reduced by just a tiny bit then the flow rate would decrease by a very large amount i would also recommend knowing that the change in pressure from the beginning to the end of the pipe if it were greater which means that the beginning and the end have a very large pressure difference this would cause the fluid to move faster and that if the length of the pipe were longer this would cause the fluid to move slower which makes sense because if you have a certain pressure difference and your pipe was very short then this pressure difference would be a lot more apparent than if the pipe was like miles long this is just recounting what i said in the last slide about turbulent flow and this equation calculates the critical speed of a certain fluid which is the speed at which point it can no longer do laminar flow and it becomes turbulent i wouldn't recommend memorizing this equation but it basically says that the critical speed is equal to some constant times the viscosity of the liquid divided by the density of the liquid times the diameter of the pipe the next concept is streamlines streamlines is the idea that you can follow individual particles from one point of its flow to another point of its flow and so to refine our understanding of flow rate flow rate is in units of liters per second which is the volume of fluid that passes through a given point per second and this is equal to the velocity of the fluid times the area that it's passing through which is equal at every single point in the streamline and this makes sense because if you have one liter per second that's flowing through here you can't possibly have more than one liter per second flowing through here or through here because you only had one liter flow through here in the first place and so this means that the flow rate is equal to velocity times area and this is the same at every single point of the pipe so if you had a larger section of the pipe the fluid would be flowing much slower than through a smaller section bernoulli's equation basically says that all of these things at one point of the fluid are equal to all of these things at another section of the fluid so to break this down this term here is called the dynamic pressure and it is equal to one half the density of the fluid times velocity squared so i remember this term by thinking about kinetic energy so kinetic energy is one-half mv squared and this is the fluid equivalent so one-half density times velocity squared the other half of this equation is the static pressure which is equal to the pressure this is just the regular pressure of the fluid times density times gravity times height and i like to think about static pressure in terms of potential energy so potential energy is equal to mass times gravity times height and so this is kind of the fluid equivalent of potential energy and this is kind of the fluid equivalent of um kinetic energy and this is just pressure so i like to think about bernoulli's equation the same way i think about energy in a solid object which is that the um mechanical energy plus the potential energy is the same for this compound no matter what and so it's the same in state one of the pipe and it's the same in stage two of the pipe this is a venturi flow meter and it was invented by a guy named venturi in order to demonstrate the bernoulli equation and so what it shows us is that fluid is moving through a large area here which means the fluid has a small velocity and it's moving through a small area here which means it has a large velocity these open pipes demonstrate how much pressure is there at any given point in this pipe so if the fluid were to rise higher then that means there's more pressure here that the fluid is exerting which allows it to rise up higher note that this h is not relative to where the pipe connects with the open pipe it's relative to a certain datum which is like an arbitrary zero point that we set so here this arbitrary zero point is set to i guess this line in the middle of the pipe so the height that the fluid rises in the open tubes is measured as this this can seem kind of counterintuitive like why wouldn't you measure it from here but if you were to construct an inventory flow meter where instead it was shaped like this you would find that this change in height would be the same for this for this pipe system where the openings are at the same height so this change in height represents the change in pressure here and what this means is that if a fluid is moving slower it actually exerts a larger pressure than a fluid that's moving faster i like to think about this as like if the fluid is running so fast through the pipe that it doesn't even have time to exert pressure on its the walls of the pipe it's just moving really really fast um and if the fluid is moving really slowly it has time to kind of like sit there and like push at the pipe um but the more scientific explanation to this is if you solve bernoulli's equation with different velocities you'll find that the greater the velocity is the smaller the pressure is because this term is greater and so the pressure term has to be smaller chapter 4.4 is very brief it's about fluids and physiology so you're very likely to see the concepts that we discuss in this chapter on the mcat in the context of the circulatory system or the respiratory system so both of these are closed loops and they both contain fluids and they both have a certain pressure a certain force is exerted on them um through your pulse or through other mechanisms and so you might see passages that require you to use these equations in order to solve for physiological concepts thank you so much for watching and i hope that this video helped you out