The question now and this is the last part is how could we possibly experimentally find the fluid flow
in a given pipe. So, suppose we have some pipe and we have fluid flowing through it like this one,
what can we do to measure the flow in this pipe? First of all, let’s introduce
a definition which is that the pressure plus the term that comes from the kinetic energy,
the pressure plus ½ ρv squared is sometimes called the static pressure of a fluid. So, we’re going to
use that to our benefit. This is called a pitot tube. We’re able to use it to measure the velocity
of the fluid flow in a given pipe. What we do is insert this into a pipe and have some sort of
measuring device above it which I’ll discuss in a second. It has two types of openings.
You see that it has a horizontal opening where fluid would try to flow into this blue area as I’ve shaded it.
It also has thinner, smaller openings which I’ve shaded in green here. So, you can see
that there’s a difference between these two kinds of openings. The important thing here is that
at the end of this pitot tube, right at the top of it, we’ve closed it off. There’s not going to be any fluid
flowing actually through the pitot tube. It actually is closed off so that the fluid flow through it
is nonexistent. There's no actual motion of water. So for example, in this blue area
and in the green area, neither of these fluids are moving in the light blue and the green area
even though the fluid in your pipe as a whole, which is represented in dark blue, is moving.
What this means is that the motion of the fluid past the green area is going to go just right past
the opening of the pitot tube that goes downwards. So, this velocity of fluid will go right past it.
You will not measure the kinetic energy part of your pressure equation. So, look at this pressure equation,
P plus ½ ρv squared. This ½ ρv squared term will not be measured by your pitot tube
in this green section because it’s only measuring the pressure to the side of the flow perpendicular
to the direction of the flow just like when we were talking about the pressure rising in a pipe
that’s having to fight gravity. That height was only measuring the pressure and not the pressure
from the fluid flow. On the other hand, this part of the pitot tube that’s going directly into your current,
even though that fluid isn’t moving, the lighter blue fluid inside your pitot tube, it does have
the velocity of the water impacting it. As that velocity of the water impacts it, it gets not only
the normal pressure of the water, it’s also experiencing the hits from the velocity of the water
as it impacts the side of the column of water in the pitot tube. So, the total pressure
in this part of the pitot tube will be greater because of the contribution from the velocity term.
So, this part of the pitot tube gets the full static pressure. All we have to do now to measure this
is hook this up to an apparatus which can measure the difference in pressures between
the green and the blue. For example, we can put a membrane or something in between
the two and measure the displacement of the membrane as it's pushed to one side or the other
because one of these pressures is greater than or less than the other pressure.
By measuring the difference in these pressures, we can solve the equation that we have written here
for the static pressure for the velocity of the water. So if we rearrange, we see that the velocity
of the water is simply related to a few variables that we can measure using our pitot tube.
We know the density of our fluid. We could know that a priori by knowing what fluid we were talking about.
The pitot tube in the apparatus above it will help us to measure the difference in the static pressure
and the pressure without the velocity term. So long as we know that term, we can solve for the velocity.
Pitot tubes are used for this reason to find the velocity of fluid flowing in many systems.