Well, we've got the flow rate.

And we've got the cross sectional area.

So we can say, this is the flow rate, volumetric flow rate,

divided by the cross-sectional area, q over a.

So let me take those 3 quantities, substitute them in.

And we get this form of the equation.

And what you'll notice right away is that I can cancel the areas.

And the numerator on both sides and we're left with this.

Which looks just like Newton's second law.

Where on the left side of, of it I have the change in pressure.

the delta P across the, the tube, which is the equivalent of the force.

I then have my mass term, which is the hydraulic inertia.

Rho l over a, and then I have the change in flow rate with respect to time.

This is the acceleration of the fluid.

So, this hydraulic inertia term,

notice that, I've got length in the numerator, and area in the denominator.

So, our hydraulic inertia is greatest for long, small diameter tubes.

So, it might be counter, counter intuitive that normally we think of just more mass.

Well, we would have more mass with a larger cross sectional area.

We actually have more.

Higher inertia with a smaller diameter area, but a long tube.

So that's where we're going to see the,

the largest inertia, like that household, water system.

Now, this plays a large roll in certain types of hydraulic applications when we

do have long, small diameter tubes.

With large changes in flow rate, like opening and closing valves very quickly.

So in those types of situations you have to pay attention to.

The water hammer effect, or the large pressure gradients that are created

by accelerating, and decelerating, and the flows.

And that it might be causing just vibrations, or

it might be causing some fatigue on the, on your hydraulic conduits.

So let's go back to that faucet example and let me take this small long tube and

attach a valve to the end of it, a faucet of some sort.

And look at what happens as far as what the pressure gradients would be,

or the pressure differential across this pipe.