Bernoullis equation can be used for a number of different situations.
In this video we are going to apply it to what is known as a Pitot Static tube.
This is an example of a Pitot static tube and the principle that it works on is that
you want to measure a pressure difference between two points where one of the points
is considered a stagnation point.
A stagnation point is when the velocity equals 0.
If we start with Bernoullis equation it says that P1 plus 1/2 times the density times V1^2
which is the velocity plus the specific weight times z1 equals the same thing P2 plus 1/2
time rho times V^2 plus gamma times z2.
We can make some assumptions that make this a lot easier.
If we say that z1 equals z2.
In other words it is horizontal we also will say that 2 is going to be the stagnation point
so V2 = 0.
What we are now left with is that P1 plus 1/2*rho*V1^2 equals P2.
We can use this equation either to solve for a difference in pressure or we can use this
equation to solve for an actual pressure given the other pressure.
Let's say that we have a plane and we have at the nose of the plane a pitot static tube.
We have far away a point.
What we want to do is find the pressure difference between point 1 and point 2.
What do we know about this airplane.
We are given that it is flying at 100 m/s, its elevation is 4000 m and we will us the
expression we developed before.
P2 equals P1 plus 1/2 *rho*V1^2.
The simplest way to do this is that P2 minus P1 equals 1/2*rho*V1^2.
We know that our V1 is 100 m/s.
We can look up the density of air at at temperature of about minus 11 degrees C.
This is 0.8194 kg/m^3.
Our delta P is 1/2*0.8194*100^2 which is 4.1 kPa.
We can also look up P1.
If we look up the pressure of air at 4000 m we find that equals 6.2*10^4 Pa or 62 kPa.