So, the second law I want to highlight now is the Conservation of Mass.

And so we know in Newtonian physics, mass is always conserved.

And, we take one step beyond this and

say that hydraulics, oil, water, is relatively incompressible.

And if I can say that mass is always conserved and I've got a constant

density and incompressible fluid, then I can

also say that my flow rate is conserved.

So if I look at a junction, which might be some t-junction in our, in our system.

It might be a cross where I have a fourth port coming out of this.

But some place where I have multiple flows coming in there.

Well, from a mass conservation perspective, I

could say the mass flow rate coming into

each one of these ports, as I add them all up, it better sum to zero.

Well, once I assume incompressible flow, now I've got these three flow

rates right here and these three flow rates better also sum to zero.

So I can say Q1 plus Q2, plus Q3, is equal to zero.

And again I've got arrows all pointing inward

so this, this all should sum to zero.

So the natural question here is, is this a good assumption or not?

Is the incompressible assumption good?

Well, typically hydraulic oils are somewhere in

w, water is well, somewhere two to

three percent compressible at the pressures we're

dealing with, so these are relatively good assumptions.

For the majority of the time, although the compressibility

of the fluid which was referred to through the

bulk modulus, does become important during some situations and

we'll, we'll talk about those later in the class.

But for now, incompressible assumption is, is a relatively good one.

So where I want to go now is apply this to a hydraulic cylinder,

so a cylinder that looks like this where I've got two different areas.

On this side, I've got my cap side.

This side I've got my rod side.

I realize that the cross-sectional area or the effective area

that the, the f, fluid is acting on is larger on

the cap side than it is on the rod side

because we've got this piston sticking out on the rod side.

And what I want to do is look at the, the

pressure and flow relationships for this, for this hydraulic cylinder.

So, first of all, from a pressure standpoint, I can say that.

If I sum up, the summation of forces is equal to mass times acceleration.

My summation of forces, well, I've got on one side a

hydraulic pressure acting, which would just be P1, multiplied by A1.

So that's this area here, which we refer to as the cap side area.

And then, acting in the opposite direction, I've got the force

acting on the rod, and as all, I also have P2.

And P2 now is acting on this smaller area right here, which is the entire

outer bore, minus the area that the rod is act, is occupying.

So we're subtracting F of the rod.