Thus far we've loo, been looking at our hydraulic cylinder and considering it an ideal component. So what we're going to look at today in this video is, what are some of the inefficiencies or energy losses that we would experience here and how do we express those when were calculating the power or the flow rate or the, the force of the actuator? So, looking at the cylinder efficiency, we've got a few major sources of energy loss. The first one is just the seal friction, and two major seals on this, this actuator, one is right up here at the rod, between the, the rod and this end cap, where we've got a wiper seal with also then probably a u-cup seal. And then between the, the piston hub which you can probably see better in the slide. And the the outer cylinder, we got another seal. Both of these have, have friction associated with them as they're, as they're in motion. We then have further viscus friction from the fluid moving through small passages within the hydraulic cylinder. So this would be a, a, a velocity related term. And then we also have, have leakage in our hydraulic cylinder, often, often leakage past the piston hub. And hopefully less leakage past the rod, but we do sometimes get leakage past the rod and, a challenge with hydraulic systems is leakage. And then some other terms that, that we won't discuss too much right now but fluid compressibility is another one we have to pay attention to. Pressure drop through the ports, especially if you're using quick disconnect ports like these that have quite a significant pressure drop. So there are many places that we could have energy loss, and we put this all together and express it in the efficiency, which is simply the output power divided by the input power. So the output power of a hydraulic cylinder is the force times the velocity, mechanical power coming out of it. The input power is the hydraulic, which is the pressure times the flow rate. Now, we take this one step further, and say let me break this up into the mechanical components, really the friction components and the volume metric, or the leakage, the compressibility components. And I can express these separately. And so, my mechanical component would, in this case would be really a, a f, force efficiency, so the force of the rod, divided by the, pressure times the area inlet. And one thing I need to stress here is that, right now I'm neglecting any pressure that would be on the downstream side. So if I have pressure coming into the, into the cap side, I'm saying that the, the pressure on the rod side would be atmospheric pressure or vice versa. So I'm neglecting that, that other pressure times area, that I'd otherwise have to pay attention to that we did in our transformer lecture. We also then have volumetric. And this primarily is leakage but also a compressibility term. And here we have the area times the velocity in the numerator. And the flow rate in the denominator. So this again is relating. How much flow do I have going into my, my cap side and what's the velocity of my rod? And I recognize some of the fluid that's going in there is going to leak past the, the piston hub. Some of it is going to go into just compressing the, the hydraulic fluid itself. So recognize that these, the mechanical and the volumetric efficiencies as they're expressed right here are not in terms of, of power but because they are dimensionless we, we're all right. And also if you multiply the, the mechanical and the volumetric efficiency. You get the total efficiency, which the ratio of the, the output power to the input power. So, let's do a, a quick example here applied to a hydraulic cylinder similar to, to this one right here. I've tried to make this as close to this cylinder as possible. On the cap side we've got a 38 millimeter diameter bore, our, my rod is about a 25 millimeter, diameter. And I'm saying I have a flow rate going into this of about 10 liters per minute at a pressure of 21 megapascals. So, I'm going to take this information a little bit of information that perhaps I can get from a datasheet about the mechanical and the volumetric efficiency of this. And from that try to calculate what the peak force and a peak velocity of this cylinder would be in extension and retraction. We'll focus on one, but we'll talk about how to do it for, for the retraction case as well. So, lemme first of all focus on an assumption that I'm going to make, and this is an assumption that the down stream or the non-pressure port is at atmospheric pressure. So, if I'm applying pressure to the cap side to drive this in extension. I'm saying that my rod side is as atmospheric pressure. So, I've got my mechanical and volumetric efficiency equations here. And what I need before I move on is the area of the cap or the rod side. I've got a diameter, I need an area. So, if I look at the extension case. The important area here would be on the cap side which is A1 on the, on the diagram and the area of the cap, would simply be equal to pi times the, the cylinder diameter. I'll put this in 3.8 centimeters. Square that, divide it by 4, and crunching the numbers, I end up with an area of 11.3 square centimeters. And this again is a lesson in paying attention to units, as we're, as we're moving through these calculations. So what I'm going to do is I'm going to take my. Mechanical efficiency equation and rewrite this, such that I can express it in terms of force. So the peak force will just be equal to the mechanical efficiency times the pressure in, which would be P1 in this case, times the area. And this will be the cap side area in this case. So, my mechanical efficiency, I've given as 92% so 0.92. My pressure is 21 megapascals, 21 times 10 to the sixth Pascals and the area of my cap is 11.3 centimeters squared but remember, Pascal is Newtons per meter squared, so we have to get. This centimeters squared into meters, meters squared. So we end up converting this, and we end up with 1.13 times 10 to the minus third meters squared. So again, just being careful of what our units are here. I can crunch this through and, and my number ends up being about 21.8 kilonewtons of force. And for those of you who are not thinking in kilonewtons yet, this is just shy of 5,000 pounds of force from this hydraulic cylinder here. So again, it shows the force density of hydraulic systems. A lot of force in a small package. So, what about the velocity capabilities? Well, to do the velocity, I'm going to simply rearrange my, lemme grab a different color here. I'm going to rearrange my volumetric efficiency equation such that I can get velocity and express velocity as the, let's see in this case I would end up with the biometric efficiency multiplied by the flow rate divided by the area. And so I plug in my numbers. I'm given the fact that I have a biometric efficiency of 95% for this case, 0.95. I've got a flow rate of. Ten liters per minute, but again we have to be careful as to what our units are here. So, I'm going to keep this in time units of, of minutes, but I'm going to convert it into cubic centimeters. So, I'm going from ten liters, which would then be 10,000, centimeters. Cubed, per minute, and, then my area is 11.3 centimeters squared. So, notice that I am not doing this calculation in pure SI units which will be meters and meters cubed per second but. Because I can, you know, have a velocity in whatever units I, I'm comfortable with this, this'll work out just fine. So, I crunch through the numbers here and I end up with 840, centimeters cubed. I'm sorry 800, 840 this would be centimeters per minute. And because that's a large number we would normally convert this into centimeters per seconds. This would be about 14, centimeters per second. All right, so we've done this for the extension case. What about the retraction? Well the only real difference that I want to highlight here is that we have to pay attention to our area difference, our, our area ratio. So, if I grab another color here and look at the retraction case. I'm only going calculate the area here because the rest of the, the work is the same, but the area on the rod side, would now be equal to pi. Multiplied by the, diameter of the, the, the, the entire bore diameter, which would be 38, or 3.8 centimeters. Square that. Subtract the, diameter of the rod at 25 millimeters, or 2.5 centimeters. Square that. And divide all this by four. So, I can say then the area of my rod, ends up being just over half of the area of the, the cap side. So I end up getting 6.4, centimeters squared. And then I could do the exact same thing and I challenge you to do so for an exercise. Calculate the exact same thing for the, for the retraction case, as I have flow going into the rod side. And we will then get a force and a velocity that are different from the extension case. But in either case, we should be able to multiple the mechanical and the volumetric efficiency to get the total efficiency, which again is the output force times the velocity divided by the pressure times the flow. So in summary here, we discussed a couple different sources of energy loss in a hydraulic cylinder. Recognize that the mechanical and the volumetric losses that we see here in a cylinder, the same thing applies to other hydraulic components such as pumps or, you know, other spool valves and things like that so we have mechanical losses, we have volumetric losses in all of those. And then we applied that to an example calculation. Thank you. [BLANK_AUDIO]