# What does the height refer to in the Bernoulli equation?

What does the height refer to in the Bernoulli equation?

I'm trying to determine the pressure on a surface where the length is short enough that the velocity should be constant across it.

Fan -> -8_________________
^-- surface


So, the idea is that there is air forced over the top of the surface and the air below it is not moving. How do I calculate this?

I've seen this equation: $$P_1 + {1 \over 2} \rho v_1^2 + \rho g y_1 = P_2 + {1 \over 2} \rho v_2^2 + \rho g y_2$$ where: $P$ is the pressure of the fluid, $\rho$ is the fluid density, $g$ is the local gravitational acceleration, $v$ is the fluid's speed and $y$ is the height of the fluid, which seems to be what I am looking for, but I'm not sure what height relates to.

• Oops, I flagged this before reading the question properly. @Moderators: PPlease decline it. – Abhimanyu Pallavi Sudhir Aug 27 '13 at 14:00

You apply the Bernoulli equation about two points, $1$ and $2$.

$y_1$ corresponds to the height of point $1$ from some reference level, and $y_2$ the height of point $2$ from that same reference level.

By height I mean vertical height, and not at some angle.

• You state some reference level. So it doesn't matter what reference level that is? I'm not sure how that works. Also, you say vertical height, but does that mean perpendicular to the surface or does that mean parallel to the force of gravity? It is because of these two questions that I posted this in the first place. – Adrian Aug 29 '13 at 12:20

At different heights, the fluid has different potential energy densities. These should be taken into consideration, along with pressure and kinetic energy density.

$y_1$ and $y_2$ are heights relative to some reference level, along the direction of gravity.

Since $\rho$ and $g$ are common factors applied on the y levels, changing the reference level will only add the same difference on both sides of the equation. When you add the same amount on both sides of an equation, you get an equivalent equation. Therefore the choice of reference level is yours. Just choose one that is practical for calculations, or that is easily understood by the intended audience, depending on the application.