0:00

So, a little bit about the pressure dropping pipes, so I am going to explain

Â why you need to have a pressure drop in order to have some drop.

Â And, I'll take you through the process the, by which you can,

Â calculate the amount of pressure drop that's going to occur in a pipe.

Â 0:24

And the relationship between the pressure and flow is determined by, the resistance

Â of the pipe or fitting or valve that the fluid is flowing through.

Â What you want is low resistance, but that

Â actual resistance is a function of the diameter

Â of the pipe or its bore, the pipe

Â length, the pipe roughness, the viscosity of the oil.

Â And then the, pressure drop is also, a function

Â of the amount of flow that goes through the pipe.

Â 0:50

Now, there are some approximate formulas that

Â have been developed that work pretty well that

Â allow you to calculate the amount of pressure drop that you have in a pipe.

Â And the reason that's important is that, by knowing the

Â amount of pressure drop you have in the pipe or conduits.

Â That will tell you how much driving

Â pressure is needed in the fluid power system.

Â 1:12

[SOUND] So the amount of resistance in a pipe depends on the type of flow.

Â So in the top plot we have and example of a Laminar flow, which is a smooth

Â flow or all the particles are moving along

Â parallel paths, and generally, that's a lower resistance flow.

Â Compared to the bottom flow, which is a turbulent flow

Â that occurs at, high velocity, or abrupt changes in direction, where

Â the flow is no longer uniform, the particles no longer,

Â are traveling in parallel paths, and the result is increased friction.

Â And increase power waste.

Â Which means that a higher driving pressure, is needed for

Â that same flow in turbulent compared to a Laminar flow.

Â So gradual changes in the direction of a pipe

Â are gradual changes in a diameter, lead you to that

Â Laminar flow, but quite a bit of the flow that

Â happens in a fluid power system, goes around sharp corners.

Â Is turbulent.

Â 2:09

The flow regime that you're in, whether

Â you're Laminar or Turbulent, depends mostly on the

Â Reynolds number, which is the, the ratio

Â of the inertial forces to the viscous forces.

Â 2:20

So here's the equation for the Reynolds number, and on

Â the top are the inertial forces, so, for example, that's the.

Â The density of the fluid, and velocity of the fluid.

Â And then, down on the bottom, is the

Â viscous forces, which is the viscosity of the fluid.

Â And you can express this either in terms of the

Â absolute viscosity, which is, the equation with the circles around it.

Â Or with the kinematic velocity, viscosity, which is

Â the, the expression on the right hand, side.

Â 2:48

That Dh is an expression of the, the size of the flow, and,

Â for a circular pipe, the Dh is simply the inside diameter, or bore, of the pipe.

Â And that's, because in fluid power, most

Â of the fluid is carried through circular pipes.

Â And you just take, Dh as being the bore.

Â 3:09

So if you've got a Reynolds number of, less than about 2,300 the flow

Â is going to be Laminar in a pipe and if you've got a Reynolds number of,

Â over 4,000 the flow is going to be Turbulent and this is going to become

Â important when you are, setting yourself up

Â to calculate the pressure drop in a pipe.

Â 3:29

So let's take a look at that pressure drop in pipes, because now

Â you have all the tools that you need in order to, to calculate it.

Â So that pressure drop is going to depend upon, the, the length of the

Â pipe, and the diameter of the pipe, and the velocity of the pipe.

Â So, what I have here is, is one equation but expressed in terms of velocity.

Â In fluid power systems, you generally don't know the velocity

Â of the flow, but you do know the, flow rate, Q.

Â So we're going to work with this equation on the

Â bottom, which is more commonly used in fluid power, systems.

Â [SOUND] So here we have the pressure drop.

Â And, let's take a look at some of the.

Â 4:11

Factors that it, it, depends on and, most importantly, let's

Â take a look at the f, which is the, friction factor.

Â So that friction factor depends on the Reynolds number

Â and on the roughness of the inside of the pump.

Â 4:25

The other factors that we have here are the density of the fluid-

Â So if the fluid is, more dense, and the, pressure drop is going to be higher.

Â The length of the pipe, so, the longer

Â pipe you have, the bigger the pressure drop.

Â And the flow rate's squared.

Â So it's very sensitive to the flow rate.

Â And then take a look at the bottom there

Â that diameter of the pipe to the 5th power.

Â So the pressure drop, is really sensitive to

Â the, diameter of the pipe that you are using.

Â 4:54

[SOUND] Getting back to that friction, factor, the the actually value

Â of the friction factors, something that has been worked out experimentally.

Â And you probably recall from, your days

Â when you took fluid mechanics as an undergraduate,

Â that the Moody diagram which is a,

Â experimentally determined chart of the friction factor f.

Â As a function of the Reynolds number and the pipe, roughness so the x-axis of the

Â chart is the Reynolds number, and y-axis is the friction factor and

Â the various curves that you have are, for different roughness of the pipe.

Â 5:31

Generally, once you know whether the flow is, Laminar or

Â Turbulent, then there are simplifying equations that are used, so

Â generally you don't have to go into this diagram and

Â pick a point, but, use some of the simplifying equations.

Â So notice over on the left-hand side, which is Laminar flow for

Â these lower Reynolds number, that the friction factor can be expressed by a.

Â Simplifying equation, which is 64 over the Reynolds number.

Â 5:58

So let's go take a look at that, for the pressure

Â drop in, pipes with Laminar flow, so here's that friction factor.

Â 65 over the Reynolds number.

Â And then, if you do a little bit of a manipulating of the equation.

Â So you've showed you so far.

Â Then, here's an equation that you can use to

Â calculate the pressure drop in a, in a pipe.

Â So, it shows the pressure drop is, proportional to the length of the pipe.

Â The pressure drop is proportional to the flow rate that you're pushing through.

Â Proportionally to the viscosity, and then down on the bottom

Â we've got that diameter of the pipe to the fourth power.

Â For example in that bicycle hydraulic hose

Â with that inside diameter of 2.2 millimeters.

Â That's going to, lead to a very big pressure drop when

Â you take that to the, fourth power down on the bottom.

Â 6:50

I'm not going to go through the formulas for the Turbulent flows.

Â Those are in the textbook that you have for the

Â course as well as most fluid power [SOUND] mechanic's books.

Â So let's take a look at an example.

Â Now, wind turbines are starting to use hydraulic,

Â or fluid power systems to carry the power from.

Â The top down to the bottom, and using a, hydraulic pump

Â at the top to, convert from the wind energy to mechanical energy.

Â [COUGH] So here on the left we've got a, schematic diagram

Â of a wind, turbine, so here's the, propeller blades up at top.

Â And they are spinning a, hydraulic pump which

Â is shooting pressurized fluid down to the base and

Â then down at the base you have a, hydraulic

Â motor that's turning a generator that creates the electricity.

Â Some of these wind turbines can be very

Â tall so current wind turbines can be 100 meters.

Â Tall or 100 meters long, so which means that

Â you've got these, conduits that are 100 meters long.

Â And so it's, important to know what

Â the pressure drop is, across this pipe, because

Â that's wasted pressure, or wasted, power that's

Â not going to be used to generate the, electricity.

Â So in this example, we've got a, a three megawatt wind turbine.

Â 8:14

And, it's running a hydraulic fluid that's

Â got a, kinematic viscosity of 46 centistokes.

Â And a density of 870 kilograms per meter cubed.

Â And that pipe is 100 meter long.

Â Run, top to the bottom of the wind tower.

Â 'Bout 20 centimeters an inside diameter smooth on the inside.

Â And then the final piece of number is that

Â the output pressure of the turbine is 35 megapascals.

Â So this gives you enough information to calculate.

Â All of the six quantities that are, asked for, here in this example.

Â Now, I'm not going to go through this example,

Â I'm not going to calculate the numbers for you.

Â This would be a great exercise for you to do on your own.

Â But what I do want to do right now

Â is to talk about you'd calculate all these numbers.

Â So the first thing is the flow rate.

Â And, you can get the flow rate by knowing

Â that the, output of the wind turbine is three megawatts.

Â And knowing that the output pressure of the, fluid is 35 megapascals.

Â And knowing that the, fluid pressure times flow is equal to the power.

Â So, with that you can determine the flow rate, and by knowing

Â the diameter of the pipe you can get the average fluid, velocity.

Â 9:36

Then you can calculate the Reynolds number

Â with the formulas that we've given you, already.

Â You can find out from, the Moody diagram or from the, general

Â guidelines that we've given you, about whether that flow is Laminar or Turbulent.

Â Then you can find the friction fa, factor if it's

Â Laminar you can find the friction factor from the simplify equation.

Â If it's Turbulence you can go into the textbook and look up

Â a simple line equation or you can pick it off the Moody diagram.

Â 10:06

Then you have all of the information to calculate that pressure

Â drop across the pipe using the pressure drop formula that we.

Â Gave you earlier.

Â And then finally, there is going to be a change in pressure

Â just from the, the height of the fluid column due to gravity.

Â So you can, take a look at how that, viscus pressure drop doing, do to driving

Â the fluids through the pipe, compares to the, pressure drop due to the, gravity.

Â So, you've got all those tools.

Â And, I would recommend that you go through

Â and calculate all those numbers on your own.

Â [SOUND]

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Â