So, a little bit about the pressure dropping pipes, so I am going to explain why you need to have a pressure drop in order to have some drop. And, I'll take you through the process the, by which you can, calculate the amount of pressure drop that's going to occur in a pipe. For the fluid to flow there must be a pressure difference. And the relationship between the pressure and flow is determined by, the resistance of the pipe or fitting or valve that the fluid is flowing through. What you want is low resistance, but that actual resistance is a function of the diameter of the pipe or its bore, the pipe length, the pipe roughness, the viscosity of the oil. And then the, pressure drop is also, a function of the amount of flow that goes through the pipe. Now, there are some approximate formulas that have been developed that work pretty well that allow you to calculate the amount of pressure drop that you have in a pipe. And the reason that's important is that, by knowing the amount of pressure drop you have in the pipe or conduits. That will tell you how much driving pressure is needed in the fluid power system. [SOUND] So the amount of resistance in a pipe depends on the type of flow. So in the top plot we have and example of a Laminar flow, which is a smooth flow or all the particles are moving along parallel paths, and generally, that's a lower resistance flow. Compared to the bottom flow, which is a turbulent flow that occurs at, high velocity, or abrupt changes in direction, where the flow is no longer uniform, the particles no longer, are traveling in parallel paths, and the result is increased friction. And increase power waste. Which means that a higher driving pressure, is needed for that same flow in turbulent compared to a Laminar flow. So gradual changes in the direction of a pipe are gradual changes in a diameter, lead you to that Laminar flow, but quite a bit of the flow that happens in a fluid power system, goes around sharp corners. Is turbulent. The flow regime that you're in, whether you're Laminar or Turbulent, depends mostly on the Reynolds number, which is the, the ratio of the inertial forces to the viscous forces. So here's the equation for the Reynolds number, and on the top are the inertial forces, so, for example, that's the. The density of the fluid, and velocity of the fluid. And then, down on the bottom, is the viscous forces, which is the viscosity of the fluid. And you can express this either in terms of the absolute viscosity, which is, the equation with the circles around it. Or with the kinematic velocity, viscosity, which is the, the expression on the right hand, side. That Dh is an expression of the, the size of the flow, and, for a circular pipe, the Dh is simply the inside diameter, or bore, of the pipe. And that's, because in fluid power, most of the fluid is carried through circular pipes. And you just take, Dh as being the bore. So if you've got a Reynolds number of, less than about 2,300 the flow is going to be Laminar in a pipe and if you've got a Reynolds number of, over 4,000 the flow is going to be Turbulent and this is going to become important when you are, setting yourself up to calculate the pressure drop in a pipe. So let's take a look at that pressure drop in pipes, because now you have all the tools that you need in order to, to calculate it. So that pressure drop is going to depend upon, the, the length of the pipe, and the diameter of the pipe, and the velocity of the pipe. So, what I have here is, is one equation but expressed in terms of velocity. In fluid power systems, you generally don't know the velocity of the flow, but you do know the, flow rate, Q. So we're going to work with this equation on the bottom, which is more commonly used in fluid power, systems. [SOUND] So here we have the pressure drop. And, let's take a look at some of the. Factors that it, it, depends on and, most importantly, let's take a look at the f, which is the, friction factor. So that friction factor depends on the Reynolds number and on the roughness of the inside of the pump. The other factors that we have here are the density of the fluid- So if the fluid is, more dense, and the, pressure drop is going to be higher. The length of the pipe, so, the longer pipe you have, the bigger the pressure drop. And the flow rate's squared. So it's very sensitive to the flow rate. And then take a look at the bottom there that diameter of the pipe to the 5th power. So the pressure drop, is really sensitive to the, diameter of the pipe that you are using. [SOUND] Getting back to that friction, factor, the the actually value of the friction factors, something that has been worked out experimentally. And you probably recall from, your days when you took fluid mechanics as an undergraduate, that the Moody diagram which is a, experimentally determined chart of the friction factor f. As a function of the Reynolds number and the pipe, roughness so the x-axis of the chart is the Reynolds number, and y-axis is the friction factor and the various curves that you have are, for different roughness of the pipe. Generally, once you know whether the flow is, Laminar or Turbulent, then there are simplifying equations that are used, so generally you don't have to go into this diagram and pick a point, but, use some of the simplifying equations. So notice over on the left-hand side, which is Laminar flow for these lower Reynolds number, that the friction factor can be expressed by a. Simplifying equation, which is 64 over the Reynolds number. So let's go take a look at that, for the pressure drop in, pipes with Laminar flow, so here's that friction factor. 65 over the Reynolds number. And then, if you do a little bit of a manipulating of the equation. So you've showed you so far. Then, here's an equation that you can use to calculate the pressure drop in a, in a pipe. So, it shows the pressure drop is, proportional to the length of the pipe. The pressure drop is proportional to the flow rate that you're pushing through. Proportionally to the viscosity, and then down on the bottom we've got that diameter of the pipe to the fourth power. For example in that bicycle hydraulic hose with that inside diameter of 2.2 millimeters. That's going to, lead to a very big pressure drop when you take that to the, fourth power down on the bottom. I'm not going to go through the formulas for the Turbulent flows. Those are in the textbook that you have for the course as well as most fluid power [SOUND] mechanic's books. So let's take a look at an example. Now, wind turbines are starting to use hydraulic, or fluid power systems to carry the power from. The top down to the bottom, and using a, hydraulic pump at the top to, convert from the wind energy to mechanical energy. [COUGH] So here on the left we've got a, schematic diagram of a wind, turbine, so here's the, propeller blades up at top. And they are spinning a, hydraulic pump which is shooting pressurized fluid down to the base and then down at the base you have a, hydraulic motor that's turning a generator that creates the electricity. Some of these wind turbines can be very tall so current wind turbines can be 100 meters. Tall or 100 meters long, so which means that you've got these, conduits that are 100 meters long. And so it's, important to know what the pressure drop is, across this pipe, because that's wasted pressure, or wasted, power that's not going to be used to generate the, electricity. So in this example, we've got a, a three megawatt wind turbine. And, it's running a hydraulic fluid that's got a, kinematic viscosity of 46 centistokes. And a density of 870 kilograms per meter cubed. And that pipe is 100 meter long. Run, top to the bottom of the wind tower. 'Bout 20 centimeters an inside diameter smooth on the inside. And then the final piece of number is that the output pressure of the turbine is 35 megapascals. So this gives you enough information to calculate. All of the six quantities that are, asked for, here in this example. Now, I'm not going to go through this example, I'm not going to calculate the numbers for you. This would be a great exercise for you to do on your own. But what I do want to do right now is to talk about you'd calculate all these numbers. So the first thing is the flow rate. And, you can get the flow rate by knowing that the, output of the wind turbine is three megawatts. And knowing that the output pressure of the, fluid is 35 megapascals. And knowing that the, fluid pressure times flow is equal to the power. So, with that you can determine the flow rate, and by knowing the diameter of the pipe you can get the average fluid, velocity. Then you can calculate the Reynolds number with the formulas that we've given you, already. You can find out from, the Moody diagram or from the, general guidelines that we've given you, about whether that flow is Laminar or Turbulent. Then you can find the friction fa, factor if it's Laminar you can find the friction factor from the simplify equation. If it's Turbulence you can go into the textbook and look up a simple line equation or you can pick it off the Moody diagram. Then you have all of the information to calculate that pressure drop across the pipe using the pressure drop formula that we. Gave you earlier. And then finally, there is going to be a change in pressure just from the, the height of the fluid column due to gravity. So you can, take a look at how that, viscus pressure drop doing, do to driving the fluids through the pipe, compares to the, pressure drop due to the, gravity. So, you've got all those tools. And, I would recommend that you go through and calculate all those numbers on your own. [SOUND] [BLANK_AUDIO]