Now that we’ve discussed ideal flow and what that is, flow rate and its conservation through continuity,
as well as Bernoulli’s principle, let’s finish up with the discussion of the Venturi effect
as well as the use of a practical device called a pitot tube. Bernoulli’s equation at equal heights
will not have any gravitational potential energy term in it because if these liquids are at equal height
in their mean, then there's no gravitational potential energy difference between the two.
So, we have a somewhat simplified Bernoulli’s equation that looks like this. But look what happens here.
If we analyze the difference between these two locations, a place that has v1 and a place that has v2.
The pressure at the second location in the thin part of this tube here is going to be equal to
the pressure in the bigger part of the tube over to the left there minus a term. What is this term?
This is a term that’s ½ ρ times the difference in the squared velocities. What this is telling us is
that the pressure in this thin part of the tube will be less than the pressure in the bigger part of the tube
because the velocity of the smaller tube is greater. So to state that one more way, the Bernoulli
sometimes are called the Venturi effect tells us that at higher velocities, you have a lower pressure
in your system. This is because the pressure that the fluid did have in this area, A1
had to go into increasing the velocity of the water. That’s where that extra energy came from.
It came from the pressure of your fluid. So, that pressure drops when the velocity of the fluid increases.
This is called the Venturi effect. You can always measure the Venturi effect by measuring the amount
of pressure that’s in your fluid by opening a small pipe over the fluid and seeing how high the fluid
raises in the air. Because as the fluid raises, it’s fighting with gravity, the height that it rises to
will depend on how much pressure is in your fluid. Since pressure 1 is much greater than pressure 2,
if the velocity 2 is greater by the Venturi effect, the pressure in the part 1 of the tube,
this wider part of the tube will show us a higher column of water. This is actually a very common method
of measuring flow rates and how much fluid is flowing in a system or flow velocities rather
by seeing how high the column of water is able to rise which tells us the pressure in your fluid.
We have an animation here of the Venturi effect. You can see that as fluid flows through a smaller part
of something that it's flowing through like a blood vessel or something else, as it goes through
the smaller location, the pressure drops but the velocity increases. This is consistent
with both the Bernoulli effect that we discussed and the Venturi effect, even though the pressure
in this fluid, it’s hard to see just by looking in this picture. But again, the velocity increases
in places where the tube is smaller and the pressure decreases in those places as well.