# Bernoulli Equation and Continuity Equation for Air Flow

In textbooks, Bernoulli Equation and Continuity Equation are typically used with Fluids. It's unclear how they can be applied to air flows.

Once thing I noticed is that since $$\rho$$ is very small for air, so we typically ignore the term ρgy in Bernoulli equation.

In the example of Pitot tubes below, I can understand the incoming air flow is brought to stop so $$v_2=0$$. But why is $$p_1$$ atmosphere pressure? Because of natural gas law and density of the air?

https://en.wikipedia.org/wiki/Pitot_tube

Another question about the above example is that seems that we cannot use continuity equation. As $$A_1$$ and $$A_2$$ are the same. But $$v_1$$ is not zero but $$v_2$$ is zero. This is fundamentally because air is compressible?

Any guideline on applying Bernoulli Equation and Continuity Equation for air flow?

• Where is $p_1$ mentioned in the Wikipedia entry on the Pitot tube? Oct 17, 2020 at 20:25
• With regard to your question about the continuity equation, none of the flow actually goes into the pitot tube. The flow goes around the pitot tube. Only the fluid velocity at the tip of the pitot tube zero. So the volume flow rate in the pitot tube (zero) does not have to match the oncoming volumetric flow rate. Oct 18, 2020 at 12:31