Pressure distributions around solid objects

[Benny]

Homework Statement

What is the $$p_\infty$$ term that arises in many expressions for pressure distributions around solid objects?

Homework Equations

An example is $$p = p_\infty - \frac{7}{2}\cos \theta$$

The Attempt at a Solution

I've seen the $$p_\infty$$ come up very often in expressions for pressure fields so I'm guessing that it's some kind of convention to put it in. Does it refer to the pressure very far away or is it the pressure at a stagnation point?

 

[anathema]

The p_\infty term in pressure distributions around solid objects refers to the free stream or ambient pressure. This is the pressure that exists far away from the object and is not affected by the presence of the object. It is often used as a reference point for calculating pressure variations around the object. In the given equation, p_\infty is subtracted from the pressure at any point to give the pressure difference due to the object. This term is important because it allows for a comparison of pressure variations between different objects or at different points around the same object. It does not refer to the pressure at a stagnation point, which is the point at which the flow velocity is zero and the pressure is at its maximum.

 

[ogb p]

The p_\infty term in pressure distributions around solid objects represents the free stream or ambient pressure. This is the pressure that would exist in the absence of the object and is typically taken as a reference point for calculating pressure differences. In the example given, p_\infty is subtracted from the pressure distribution to account for this reference pressure. This term helps to normalize the pressure distribution and make it easier to compare between different objects or flow conditions. In some cases, p_\infty may also represent the pressure at a stagnation point, but this is not always the case.