Now that we have a definition for flow rate, we’re going to go to an idea of continuity
and how flow behaves as the system that it's flowing through changes, whether it’s getting narrower
or more expansive, et cetera. If this is happening, let’s first take a simple case where there’s no
expansion or contraction. We won’t quite get to the junction that are drawn here yet.
Let’s just assume a normal flow. In this case, we can say that the flow rate must be conserved.
This is just a way of saying that mass is conserved. The mass, the fluid can’t be leaving
or disappearing anywhere. For example, in these two cylinders of fluid that I’ve drawn,
the first cylinder if it had a slower flow rate or less flow rate would lag behind the second cylinder,
the fluid that was right in front of it. It would start creating a vacuum. There would be an opening
opened up in your fluid because some of the fluid is lagging behind. This is not at all a physical scenario
that little vacuum bubbles would open up and blood vessels are anywhere else.
Similarly, if it was too fast, if there’s too much flow for the fluid behind, the fluid in front of it,
there would be an overlap and you would have two particles occupying the same place at the same time
or at the very least a great increase in the pressure in that small area. Again, this is not at all
a physical situation. We need that the flow of any part of your fluid to any other part
is exactly the same as identical. We have a conservation of fluid flow. To summarize this
because it is a very key point. This is really important to understand that fluid flow is conserved.
We can say that the flow rate, again represented by Q which is the cross sectional area
times your velocity is conserved by conservation of mass. We also know that Q, as I said,
is A times v which means that if we change A, now that we’ve passed this junction here
from a bigger cross sectional area to a smaller cross sectional area, we know that if these fluid flows
must be the same, A1 times v1 is equal to A2 times v2. While A has changed dramatically,
then just by looking at this equation on the far right here, A1v1 equals A2v2, imagine to yourself
that A2 has become a very tiny number. That the flow area that it's able to flow through
has constricted greatly. If these two sides of the equation are still going to be the same,
if A1v1 is still going to be equal to A2v2, the conclusion is that v2 has to increase.
The flow speed, the velocity of your flow has to increase greatly if it’s going to go through
a smaller part of your system. This is a key, key point to know that the velocity is greater
in places with lower cross sectional area for the reasons that we just discussed.