Ch 17: Fluid MechanicsSee all chapters

Sections | |||
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Density | 34 mins | 0 completed | Learn |

Intro to Pressure | 76 mins | 0 completed | Learn |

Pascal's Law & Hydraulic Lift | 28 mins | 0 completed | Learn |

Pressure Gauge: Barometer | 14 mins | 0 completed | Learn |

Pressure Gauge: Manometer | 15 mins | 0 completed | Learn |

Pressure Gauge: U-shaped Tube | 23 mins | 0 completed | Learn |

Buoyancy & Buoyant Force | 64 mins | 0 completed | Learn |

Ideal vs Real Fluids | 5 mins | 0 completed | Learn |

Fluid Flow & Continuity Equation | 22 mins | 0 completed | Learn |

Additional Sections |
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Bernoulli's Equation |

Concept #1: Intro to Density

**Transcript**

Hey guys. So now we're going to start talking about fluids which is also sometimes referred to as fluid mechanics, fluid dynamics or just liquids. Now the first topic you need to know really well is density. So let's jump right Into it. Alright, So liquids and gases are types of fluids, types of fluids. So liquid is a fluid and a gas is a fluid. So we're going to use the term fluids to refer generally to both liquids and gases and the reason we do this is because liquids and gases behave very similarly in a lot of different situations. So instead of saying liquids and gases, liquids and gases all the time we're just going to say fluids which refers to both things, cool? So density is the first big concept we have to understand and you may remember density from chemistry class, the density material has to do with how tightly packed the molecules are. So, for example, here you've got the same sort of volume this sort of blue cup and it's got these little green balls here they're not very packed together. So we're going to say that this is low density and here they're very tight together. So this is going to be high density, okay?. So the more compressed things are the higher density you have, density in physics is given by the letter, by the Greek letter Rho, Rho which is a little P, a curvy P and if you remember it's simply mass divided by volume, mass divided by volume. So mass in physics is always kilograms and volume in a three-dimensional length. So it's going to be cubic meters, so it's kilograms per cubic meter. remember if you have the three dimensions of an object like a rectangle or something, then the volume of a rectangle would be the width of the rectangle times the height times the depth, right? And sometimes you see length instead of one of these three measurements and because each one of these guys is a meter you get meter, meter, meter, you have cubic meter, cool? Now sometimes you are given the density and you're given these dimensions, right? So you're given density Rho and you're given the three dimensions, whenever you're given the three dimensions you're able to find volume and if you have Rho and volume, if you have Rho and volume then you're going to be able to find the mass, and that's because of the equation, Rho equals mass divided by volume therefore if I move the V up here, I hope you see that right away, you get m equals Rho volume. So let's put this over here, mass equals Rho volume, right? And they try to trick you with this but it's very straightforward, it's just a play on this original definition here of density. Sometimes you see something that says that objects have the same material, in density problems this usually means that they have the same density, okay? So if you have a, if you have two pieces of wood and we say it's the same kind of wood you can also infer that they have the same, you can conclude that they have the same density, cool? And then the last quick point I wanna make and then we'll do an example is if you have liquids in a container, two liquids or more liquids, two or more liquids in the container, the liquid of the higher density will be at the, what do you think, top or bottom? Higher density liquid will be at the bottom, okay? The higher density liquid will be at the bottom and you can think of this as higher density being heavier. Now I'm putting this in quotes because it's not necessarily heavier, it's going to be heavier depending on what you have more or less volume of it but on a per molecule basis it is heavier or per small area or per small volume it is heavier therefore it's going to go to the bottom because liquids can sort of move around. So you might have seen something like this where they put all kinds of different things and you can see them becoming very different. So there's a heterogeneous mixture here and honey is all the way at the bottom which means honey is the the highest density out of all these things that are here, cool? So we'll see some stuff like that later let's do a quick example here. What is the total weight of air molecules inside a large warehouse, and they give you the dimensions here. So I went to total weight of air, right? So air does have a weight and, so first let's start with weight, weight remember is just mg mass times gravity and I know gravity, I'm going to use here just for the sake of keeping it simple let's say gravity is approximately 10 meters per second squared. So I'm going to use 10. So if it's asking you for weights and I know gravity all I really need is mass. So this question is really about finding the mass of air in this space. Now I'm giving this, right? So you can sort of draw this it's 100 wide, 100 deep. So it looks something like this, not to scale, okay? So this is 100 meters here, 100 meters here and 10 meters high, whenever you can three measurements you can right away find the volume, volume is just those three measurements together multiply 100 times 100 times 10 and here you just count the zeros, those are five zeros. So this is 10 to the fifth and I got meter times meter times meter. So cubic meter, right? Or you can write it out if you want, one, two, three, four, five. So it's a hundred thousand cubic meters, okay? Now, I have the volume, I have the density right here. So I can find the mass because remember density is mass over volume, I have the volume, I have the density, it was given right here. So we can just find the mass which is the equation I showed you just a few moments ago. So Rho, V and then you're going to multiply the two, Rho is going to be 1.225 kilograms per cubic meter, I highly recommend you put the cubic meter down here, right? But don't put it over here, if you put it in the bottom it's going to be easier to play with it times the volume which is 100,000 cubic meter, and then notice what happens here, right away this cancels with this, and you've just got this big multiplication. The mass therefore is going to be, if you put this in the calculator you're going to get 122,500 you're left with kilograms, a little bit of dimension analysis here cool. Are we done? No because we're getting mass. So that we can plug it in here and get the weight but that's the last step I'm going to do here weight is mass times gravity and I just have to multiply those two, we're getting as gravity as 10. So we just have an extra zero here. And the unit for weight since it's a force is newtons. So this is a million newtons of weight cool? So the air in this entire thing is actually pretty heavy, if you would put that entire air on top of you it will crush you in a very small amount of time. Alright, cool, let's do this example here, if you want you can pause the video and give this a shot yourself, I'm going to keep rolling here it says the density of whole blood. So whole blood means it's all the different parts you have of your blood, plasma everything else, is nearly this. Now in physics whenever they say a value is nearly or approximately we're just going to use that value. So density is Rho of whole blood is 1.06 kilograms per liter, I'm going to write it like this. Notice that it didn't say kilograms per cubic meter instead of said per liter and these two are not equivalent but they are related and we'll talk about this in a future video. So we're just going to leave it like that for now, and then says, how many kilograms are in a pipe pint of whole blood. So asking how many kilograms, kilograms is the units for mass, if I say how many kilograms I'm asking for the mass. So what is the mass and I'm given the volume here, the volume is 473 milliliters. Now you can't really use milliliters, you're supposed to use liters but let's leave it alone for now let's not sort of prematurely convert units here. Alright, so this is very straightforward, I have three variables that are related by this equation, by the definition of density which is mass over volume, I want to know mass, I have the other two, I just have to move things around, this question is a little bit more straightforward than the other one, p,v or Rho,V and this is 1.006 kilograms per liter times the volume which is 473 milliliters. Can't really do this without changing either liters into milliliters or milliliters into liters, hope you remember this is very straightforward one liter is a thousand milliliters, I'm actually just going to scratch this and put 1,000 milliliters, right here, milliliters will cancel and then you're left with kilograms which is what you want. So all you got to do here is multiply this big mess and if you do that you get 1.06 times 473 divided by 1,000 and this is going to be in kilograms and you can do this in a calculator, you get 0.501 kilograms. That's how many kilograms or how much the mass of the, mass of bloods, of whole Bloods if you have one pint of it with this density, cool? That's it for this one let's go to the next one.

Concept #2: Density Values & Specific Gravity

**Transcript**

Hey guys. So in this video, we're going to talk about some values of density you should know as well as specific gravity, let's check it out. Alright, so you should know certain values and units for density. So you should know that fresh water is 1,000 kilograms per cubic meter what this means is that if you have a cubic meter, a cubic meter of water, right? So you fill it out with water, that's going to have a mass of 1,000 kilograms which is over 2,000 pounds, okay? So pretty heavy stuff. So 1,000 kilograms for every cubic meter and you can also rewrite this as one kilogram per liter, that means that every kilogram of, every liter of water has a mass of one kilogram or one gram per cubic centimeter that means that one cubic centimeter tiny little amount of water is one gram of water, cool? So I if you remember these you got two benefits one you know the numbers for water but you also can use this as a way to convert stuff. So, for example, if you know that a thousand kilograms per cubic meter is one kilogram per liter and then I give you 1.2 kilograms per liter, you can immediately convert that and say, well, if one here is 1,000 here then 1.2 of this must be 1,200 of the other, okay? So this allows you to make some quick conversions by remembering what the ratios are. Now you have fresh water and you have saltwater and this is pretty straightforward but just in case, I have here anytime you the question refers to a lake a river or house water meaning water coming out of a faucet or whatever, it's going to be fresh water and fresh water is the default water, if you're not sure if it's fresh or salt it is fresh, okay? And it's 1,000 it's the easiest number out of all of these to remember, salt water is water you put some salt in it and it's water from the ocean, right? Seawater. One way to remember this is, imagine if you have water and you pour some salt on it, now it is denser therefore it's a little heavier, that's why it's 1,030, okay? Just a little bit heavier. Whole blood, whole blood when you have plasma and all the other crap that's in your blood and that's going to be 1060. Air, air is 1.2. Now this is not a typo or some weird mistake, air is in fact 800 times, this is a thousand, this is 1.2, this is about 800 times lighter than water and that makes sense, right? Air is much lighter than water, if you have a huge box with a bunch of water that can be very heavy if you have a huge box, let's say a cardboard box and it's got a bunch of air in it it's not going to be very heavy, it's also why when you look at the horizon you see water at the bottom, right? If you're looking out of the ocean and the air at the top because air is lighter so it is on top, it's pretty silly but, that's how it is, Cool. You should know that oil and wood are usually going to be slightly lighter than water a lot of the measurements for oil and wood end up being about a 800 kilograms per cubic meter instead of a thousand so it's a little bit lighter, those are pretty popular in fluid problems and the last thing I want to talk about before you do an example is I want to give an idea of what these measurements are. So you could have a volume at something like centimeters, centimeters cubed or cubic centimeters or cubic meters which are lengths, right? But then it's cubes so it's a volume or you can have in terms of liters or milliliters which are more readily identified as being volume and I want to give you a sense of what these things are. So a cubic centimeter, a centimeter is like tiny like this, right? It's less than half an inch. So to the centimeter is a tiny little cube and that's one milliliter of water, right? So it's this guy right here okay, this is one cubic centimeter or one milliliter of water. Now this is what one milliliter of water looks like, it's a tiny amount of water two liters of water is your big water bottles, right? And, this is what one cubic meter looks like. So here's a dude this guy the average person is probably, I don't know 1.8 meters, right? So you would have a box a 1 cubic meter box would be about a half way up to where you are and it would be this just big box here and that this would have 1,000 litres 1000 litres of water or whatever, right? So the idea here one point that I want to make is that one cubic meter is gigantically bigger than a cubic centimeter section million times bigger, cool? Alright, let's do a problem here a quick example how much does 500 milliliters, that's a volume, so volume equals 500 milliliters of a 2.3 grams per cubic centimeter, so what is this, well, this is a mass, and thi is a volume, mass over volume is our density. So the density it didn't say density, you have to figure out by the units there, it's 2.2 grams per cubic centimeter and I want to know, how much does that liquid weight? in other words what is the weight of that liquid which is mass times gravity. Now, we know gravity, we're going to use 10 here just to make life easier, we know gravity. So really this question is asking us for mass, if I can find the mass, if I can find the mass I will find the weight, how do I find mass? Well, if I have V and Rho density and I want mass I can just use the density equation, density is mass over volume therefore mass is Rho, V and Rho is 2.2 grams per cubic centimeter. Remember always draw, always write it in the bottom so it's easier to see, times the volume which is 500 milliliters, okay? So there's all kinds of problems here with the unit's that we're going to have to try to fix, this here is a volume, this here is units of volume as well, but they're not necessarily compatible with each other or at least they're not the same exact thing, right? Milliliters and cubic centimeters. So, can we convert one to the other? and if you remember this piece here, if you remember that one cubic is in fact one milliliter then you know that these two are equivalent, they're not the same but they're equivalent so they can be canceled and then you're left with 2 times 500 2 times 500 which is 2.2, so it's 1100 grams, but we cannot read this in grams, we have to turn it into kilograms so this is just going to be divided by a thousand. So it's gonna be 1.1 kilograms just some quick dimension analysis there or really just conversion using the metric system, right? So 1.1 kilograms, are we done? Not really, that's the mass so we can find the weight, weight is mass which is going to be 1.1 kilograms times gravity which is going to be 10 meters per second squared so this is going to be 11 Newtons, cool? So that's it for that one. Now, let's talk about specific gravity real quick and some professors will talk about specific gravity some won't, if you've never heard this, if you've never seen this in class you could skip it but specific gravity it's just a term that's related to density, it is density relative to water, it's kind of a silly idea but you should know it if your professor cares about it. So the definition of specific gravity SG. So the specific gravity of something is the density Rho of that something divided by the density of fresh water and by the way density of fresh water is 1,000. So I can simply rewrite this and say that specific gravity of something is density of something divided by 1000, that's it, just take density divide it by 1,000. So, for example, what is the specific gravity of fresh water, well, specific gravity of fresh water, you have specific gravity of fresh water is the specific gravity is the, I'm sorry, it is the density of fresh water because this guy here goes on the top, so this matches up with this, right? The specific gravity of X is the density of X. So the specific gravity of fresh water is a specific density specific water divided by, the definition of the equation is at the bottom is always a fixed number which is the density of fresh water, so this is kind of silly because it's just 1. Because specific gravity is relative to fresh water the specific gravity of fresh water is 1 because it's the same, okay? So, what the heck is its and used for, well, if you know that the specific gravity of something is 1 that means that it's because it is twice as dense as fresh water and you would immediately know oh that means that the density is 2000 if the specific gravity of something is 0.7 it means that it's 70% of water which is a thousand. So this would mean that the density is 700, okay? It's a little silly, they could have just left it at density but there's other term you should know, let's do an example, here it says, what is the volume of a wooden cube. So I want to know what is the volume of a wooden cube with a specific gravity of 0.8, so the specific gravity is 0.8 that weighs 16,000 Newtons, so the weight is 16,000 Newtons, what is the volume, okay? So can we do anything here? So where are we going to get the volume from? well, there's specific gravity which is related to the idea of density and weight is related to the idea of mass, right? There's equations that connect these two. So if you have volume, density and mass you can put them together on the density equation, density is mass over volume therefore if I move some things around volume is mass over density. So if I can find the mass and if I can find the density I can find the volume. So let's see if we can do that. So, first let's try to find the density. So the specific gravity of something is the density of that something divided by 1,000. So I can just move things around find the density of something in the specific gravity which is 0.8 times a thousand which will give us 800, it's very similar to what I did up here, right? The 0.7 became 700 the 0.8 It becomes 800. So I got the density. So let's see if we can find mass. So weight, remember is mass times gravity and if I know the weight but I want mass I can just move things around mass is weight divided by gravity, so it's 16,000 divided by, we're using 10 so this is 1600. So, now we can plug stuff in, the mass was 800 and the density, I'm sorry, the density was 800 and the mass was 1,600, got that backwards there, the mass is 1600 and the density is 800 and if you do this, this is simple I made the numbers easy here it means that the volume is true. Now what are the units? The units are cubic meter, why? Because we have standard units, this was 1600 kilograms, okay? 1600 kilograms because we were dividing, because we're dividing Newtons my meters per second squared, so we're using standard units and then you get a standard unit and here, this was kilograms per cubic meter, okay? So long story short whenever you using standard units you get standard units, the standard unit for volume is cubic meter. So you get a cubic meter. So the answer here is 2, that's it for this one, let's keep get going.

Practice: A wooden door is 1 m wide, 2.5 m tall, 6 cm thick, and weighs 400 N. What is the density of the wood in g/cm^{3}? (use g = 10 m/s^{2})

Practice: Suppose an 80 kg (176 lb) person has 5.5 L of blood (1,060 kg/m^{3} ) in their body. How much of this person’s total mass consists of blood? What percentage of the person’s total mass is blood?

Practice: You want to verify if a 70-g crown is in fact made of pure gold (19.32 g/cm^{3} ), so you lower it by a string into a deep bucket of water that is filled to the top. When the crown is completely submerged, you measure that 3.62 mL of water has overflown. Is the crown made of pure gold?

Suppose the vessel containing the water and the ice is full: The water level is at the vessel’s rim. What happens once the ice melts?
A. The water overflows.
B. The level of the water remains at the rim.
C. There is not enough information given, the outcome is not definite.
D. The level of the water drops below the rim.

A cylinder, 16 cm long and 3 cm in radius, is made of two different metals bonded end-to-end to make a single bar. The densities are 4.4 g/cm3 and 6.3 g/cm3. What length of the lighter-density part of the bar is needed if the total mass is 2377 g?
1. 9.92098
2. 13.1373
3. 7.52775
4. 12.5493
5. 11.7805
6. 10.4417
7. 9.5286
8. 9.69549
9. 8.8057
10. 10.0839

One cubic meter (1.0 m3) of aluminum has a mass of 2700 kg, and a cubic meter of iron has a mass of 7860 kg. Find the radius of a solid aluminum sphere that has the same mass as a solid iron sphere of radius 4.77 cm.

A piece of pipe has an outer radius of 4.7 cm, an inner radius of 2.8 cm, and length of 32 cm as shown in the figure. What is the mass of this pipe? Assume its density is 7.8 g/cm3.

An ice cube floats in a glass of water. As the ice melts, what happens to the water level?a. It rises.b. It remains the samec. It falls by an amount that cannot be determined from the information given.d. It falls by an amount proportional to the volume of the ice cube.e. It falls by an amount proportional to the volume of the ice cube that was initially above the water line.

How long are the sides of an ice cube if its mass is 0.45 kg? ( Express your answer to two significant figures.)

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