So in this lecture we're going to discuss fluid power variables, specifically pressure and flow rate and use them to calculate power. We're also going to talk about the difference between a through and a cross variable and how that, how that and how that relates here. So first of all pressure. Pressure is simply the force per unit area. And one thing I want to stress here is that, unlike a solid where you can have tensile force or tensile stress, a fluid can only be in compression. It cannot handle a tensile stress. And so, these pressures were talking about are always a compressive. Pressure in the fluid itself. Now, our pressure is what we refer to as an across variable and the reason for that is that it's always measured with respect to something else. So what do we measure it with respect to? Well often we, we measure with respect to atmospheric pressure, in which wa, case we refer to it as gauge pressure, sometimes we measure it with respect to vacuum, in which case we call it absolute pressure, sometimes we'll talk about the pressure drop across the valve. And in that case, it'll just be a delta p or pressure differential from the upstream side to the downstream side and that would be the pressure difference. But again, always measuring with respect to something else and therefore talking about it as an across variable. So, one thing you're going to find in this class is that units can be quite challenging in fluid power. And the reason for that is yet we have to deal with both SI and U.S. customary units. And you might say you know, you might be in another part of the world where you're not dealing with, with U.S. units of a regular basis but in fluid power you have to because so many manufacturers are in the U.S. so many OEMs are in the U.S. and you have to jump back and forth between, between unit systems. So we're going to talk about both unit systems in this class. The one thing I'm going to stress is that I recommend doing your calculations in the SI system, we'll talk about why in just a moment. So the SI unit of pressure is Pascal's. So a Pascal is a very small unit and so, when we're often using this for fluid power we refer to this as Kilo Pascal's. Or Mega Pascals. Now, another common non-SI unit is a Bar and one Bar is simply equal to 100 Kilo Pascals. Now the reason this unit nice is because a 101.3 Kilo Pascals is atmospheric pressure, so a bar is very close to atmospheric pressure. So if you talk about 200 Bars of pressure, you're at approximately 200 times atmosphere. So it, it makes it a little bit easier to, to relate that pressure. Now, in the US customary system, we refer to it in pounds per square inch, or PSI. And, this is uniformly used. Sometimes in, in large water systems, you'll have pounds pounds per square foot. But PSI is, is the most common for. High pressure fluid power systems. Now our other major variable we're dealing with is flow rate, and we're going to need to talk about both volume metric flow rate and mass flow rate. And, flow rate is simply the volume or mass per unit time, and we refer to this as a through variable or the flow across an imaginary plane. So if you can imagine I've got this water spigot here and let me draw a plane right here. Or I can look at either the method that's flowed across that plane or the volume that's flowed across that plane per unit time, per second, per minute, whatever unit we're linking, looking at. So, one thing we have to be careful of here is whether or not we're talking about a compressible fluid or an incompressible fluid. So for hydraulic fluids that we normally think about as incompressible, meaning the density stays constant. We can either use mass flow or volumetric flow. Volume flow is easier to measure, so we normally report it in that, in that way. And so the vol, units of volumetric flow rate in the SI system are cubic meters per second. Cubic meters per second is an enormous volume. And so normally we have to reduce this to, to smaller units that, that we can deal with. And this typically. Used in, in liters per minute is a more common measurement, but again non SI. Now in the US system Gallon per minute is a, is a very common unit of measure though you sometimes you also see cubic inches per second but again not, not uses as often as having to convert from cubic meters per second in the, in the SI system. Now, pneumatic applications, where we have gas as our, as our working fluid, there we have to measure the mass flow rate because the fluid is compressible. The density is changing, so we can't just rely on the, the volumetric flow rate. So, when we're doing mass flow rate, our units in the SI system are kilograms per second. And in the U.S. system, our pounds mass per second. So again be careful whether there's pounds mass or pounds force. In this case, it's a mass flow rate. So pounds mass per second. So how do we measure pressure and flow? Some of the most common devices for measuring pressure is just a, a pressure gauge, it looks like this, where we've got an input port right here. This is a pipe thread in this case, and then we've got a dial that swings a bolt through a, a pressuring bar and pressuring PSI. And we can just use this to quickly glance at the system and say, what's the pressure operating at, at this point? And it also gives you a, a nice feeling of what's the time history, because you can watch the needle bouncing around if there's pulsations in the flow. Now, if you need to acquire the signal either in a computer or a microprocessor for some reason, you would typically then use a pressure transducer which looks like this. And again, a port right here, I've got. Four electrical leads on this side. And what's going on her is we've got a metal diaphragm. The pressure acts on that diaphragm, creates a strain. I've got strain gauges on the diaphragm and as those strain it changes the resistance. We have a wheat stone bridge inside of there. We amplify the milivolt signal into a voltage signal that we can send to the, to the computer. So this allows us to convert a pressure, into a voltage or a current that we can read in a computer or micro-processor. Now, for measuring flow, there's a number of different devices. One of the simplest is what we call a rota meter. And this is an example of a rota meter and you can see this little slug that is sliding back and forth. So this tube shaped area in here is conical so it's smaller diameter to the bottom, larger on the top. I've got flow coming in, coming out up here. So, I've got gravitational force acting downward. And the viscous force of the fluid acting upward. When those balance, the slug stays in one location, and I can measure the pressure off the top of the, that slug. Other ways to measure volumetric flow rate are gear flow meters, Coriolis flow meters. There's a whole lotta other types, like the, the turbine flow meter that's shown here on the slide. Many other ways of, of measuring flow rate and then there's also some that will, will measure mass directly. So a variety of ways, just a sampling that you'll see right here. We'll talk about more when we get to, to the lab. So some power calculations. Now I was mentioning that I recommend doing your, your calculations in the SI system. Let me illustrate that now. Power in hydraulics is simply the pressure drop times the flow rate. So, maybe I've got a hydraulic power going into my actuator, I've gotta know what the, the pressure drop is, so I need a reference pressure. Perhaps it's atmospheric pressure. And so I've got a pressure and a flow rate going in to here, so I can calculate the hydraulic power entering that device. And, let me throw some, some numbers in here just so that we can, can provide this example. So, in the SI system, let me give you a pressure where are delta P might be 21 Mega Pascals and our flow rate let's use a value of just let me get my numbers here of 12 liters per minute. [BLANK_AUDIO] Now remember that I said the base unit in the SI system for flow rate is cubic meters per second so I'm going to convert this into cubic meters per second. And this flow rate ends up being 2.04 times 10 to the minus fourth cubic meters per second. So now when I do my power calculation, this is just equal to the pressure drop times the flow rate. So my pressure is 21 times 10 to the 6th Pascals, which is a Newton per meter squared. Multiply this by my flow rate, which is 2.04. Times 10 to the minus fourth cubic meters per second. I multiply these together, and I end up with just over 4 Kilowatts. 4,284 Watts. And one thing I always recommend doing when ever you get done with one of these calculations is verifying that your units worked out. And so we can say what is a, what is a, a Watt in this case? A Watt is just equal to a Newton meter per second, and we see that we do have Newtons in the numerator, I've got newtons cubed divided by meters squared, so I've also got meters in the numerator. And seconds in the denominator. So my units do work out. Now let's try to do this in the, in the US system. So first of all, I need to say that my horse power. Is the unit of power. And this 550 foot pounds per second. A little bit odd number but again, created when horses were doing the majority of the work. And now my power calculation. Let me first of all give my, my pressure drop in standard units of PSI. So 21 Mega Pascals, approximately 3000 PSI. And my flow rate of 12 per minute ends up being about 3.2 Gallons per minute. So now, when I multiply all those together to get my power. My power is my pressure of 3000 PSI, pounds per square inch times my flow rate of, pardon me 3.2 Gallons per minute. And now I've got to do a bunch of unit conversions to get me to the units that I want to be in. So I've all ready got. Pounds, which is what I need for foot, pounds per second. But I'm in minutes and I'm in gallons and I'm in, in inches squared, so I need to do a few unit conversions. So first of all let's say that 1 foot is equal to 12 inches. And then I can say that gallons to cubic inches is 231 inches cubed for gallon. Then I need to convert time, and I can say one minute is equal to 60 seconds. And finally, I can convert my power into a unit of horsepower. So, I can say that one horsepower. Is 550 foot pounds per second. And finally I can crunch through this and say this is 5.7 horsepower. So, notice all the extra steps to do all these unit conversions when we're doing this in the US system. That's why I recommend doing your work in the, in the SI system. It will make your life much easier in the long run. So, in summary with this video, what we've talked about is first of all pressure. The measurement of pressure, the measurement of flow rate as through and across variables. We then talked a little bit about how to measure them with these various devices of pressure transducers, roto meters. And then talked about how to do pressure calculations as just the pressure times the flow rate. I'm sorry, power calculations as the pressure times the flow rate. Thank you. [BLANK_AUDIO]