Folks, in this video, we're going to talk about 2 important terms when it comes to fluids in motion. We're going to talk about fluid speed and volume flow rates. Both of them are really important; they sound kind of similar. I'm going to go ahead and break down the difference between the 2 and we'll do a quick example, alright? So these two main terms deal with basically how quickly a fluid flows. So, fluid speed is pretty straightforward because we've dealt with speed before. Remember, speed is always just meters per second. It's a distance over time. So this would be literally like how fast a water molecule is traveling through a pipe. So the velocity is given as ΔxΔt. Basically, if you could track a little water molecule as it flows through this pipe like this and if one of them was traveling faster, then basically this would have Δx1, this would have Δx2 and if both of these water molecules had the same Δt, let's say it was just one second, then what this means here is that the velocity of the second molecule because Δx2>Δx1 would be greater than the velocity of the first one. It's pretty straightforward. Basically, it's just how fast something is moving through an actual pipe or something like that. Alright. Now the other one is going to be volume flow rate, which is a little different. We haven't heard that one before, but it's tricky because sometimes rate and speed are sort of generally used to mean the same thing. But speed is going to be meters per second, but rate is basically how fast something is changing. The thing that's changing here is going to be the volume. So the equation for this is actually going to be or the units for this is actually going to be meters cubed per second. Notice how this is meters per second, right? It's distance over time, but this is actually units of volume per seconds. So the unit or the letter that we use for the volume flow rate is actually going to be Q and what this is ΔVΔt. Alright. So this would be like if you had one water molecule that was traveling through a skinnier pipe like this, and then you had another water molecule that was traveling through a much larger thicker pipe like this, even though their speeds are the same. So they're so in this case, the Δx1, Δx2 are the same. It's just the same Δx, so therefore, v1=v2. There's something that's significantly different about this thicker pipe here, which is basically the volume of water that's passing through it in a certain amount of time is much larger. If you take a cross sectional area of this pipe like this, then basically all the water that's going through this pipe is everything that I have shaded in this region over here. Right? I'm going to go ahead and label this or highlight this in yellow. Alright. So all of this water here is passing through. In the same exact amount of time in the skinnier pipe, you have a much smaller volume of water because the cross sectional area is smaller. Notice how the amount of water that flows through this one second is only just this piece over here. So basically, that's what's different about these 2. Even though their speeds are the same, their fluid speeds, their volume flow rates are different. ΔV2>ΔV1, and that's basically just because you have a bigger cross sectional area. Alright? So one thing I want to do with this equation here is sort of rewrite this. Remember that ΔV or remember that volume can generally be written as area times height. Right? So in other words, this is the Δx and to this cross sectional area over here of this cylindrical pipe is going to be A. These two things combined, the area times the Δx is what your volume is equal to. So this volume here is equal to A×Δx. So you can rewrite this equation as A×ΔxΔT. Now notice something weird happens because we have an area times ΔX over ΔT. Remember, that's just the definition of velocity. So in another way, you can rewrite this equation is that it's actually equal to A×v. So I want to point out here that this capital V, this ΔV for volume is an uppercase V. So this is uppercase V, whereas this one is a lowercase v. So this has to do with the velocity. Alright. So don't get those confused. But basically, what this means is that you can actually rewrite this ΔVΔT as the area times the velocity. Alright? So it's kind of a sort of a little confusing there because you have a big V and a little v, but you can essentially rewrite the volume flow rate in terms of the fluid speed. Alright? So these are going to be the equations that you use, basically throughout your fluid flow problems. Alright? So let's go ahead and just take a look at an example real quick. It's pretty straightforward. So we have a long horizontal pipe, it's got a 2 meter section a cross sectional area. So in other words, we've got this area over here. This A is equal to 2. Alright, so we've got, it takes 5 seconds to travel an 80 meter segment of the pipe. So basically, I'm going to say is there's a water molecule here. It's going to travel some distance and I have that this distance here is going to be Δx=80. Alright, and so what happens here, I want to calculate 2 things. I want to calculate the fluid speed and then the volume flow rate. Let's take a look at the first one here. We're going to calculate the fluid speed here. Remember that fluid speed V is just ΔxΔt, so straight up distance over time. It doesn't take into account the amount of water it's flowing. It's just how long does it take one molecule to get from one place to the other. And it's pretty straightforward. We have that Δt is just equal to let's see. It was 80 meters in 5 seconds. So in other words, this is just going to be 80 divided by 5 and what you're going to get is 16 meters per second. Alright, so that's just straight up what the speed of this liquid running through is. Now, let's take a look at the second part here. We're going to calculate the volume flow rate. Remember that that's going to be Q and Q is equal to 2 things. We have ΔVΔT, or you can rewrite this in terms of area times the velocity, terms of basically area times this fluid speed over here, which we just found is just 16 meters per second. So in other words, we can rewrite this and say we have the cross sectional area. The area is just 2 over here, and that's just going to represent all of the volume over here. That's ΔV and this is just going to be 2 times 16. Notice how let's see. Let's write out the units. We're going to have 2 meters squared we're going to have 16 meters per second, and what you end up with here is you end up with 32 meters cubed per second. Alright? So even though the fluid speed is only 16 meters per second, the amount of volume that passes through this pipe in that time is 32 meters cubed per second. Alright, so that's the distinction. Hopefully that makes sense the difference between speed and volume flow rates.
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Fluid Flow & Continuity Equation
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