#Mechanics # What is a Fluid? Intro A fluid refers to substances which can flow and have molecules which can change position under pressure. Armed with this definition, it's good to note that not just liquids are fluids! Heck, fluid dynamics kids have nightmares about their reliance on fluids to survive - so let's avoid that, shall we? # Fluids at Rest If you haven't already, I've put basic pressure-density calculations in the [[Newton's Laws and SUVAT#Pressure and Density|fundamentals document]]. This is an almost direct extension of this - so it's imperative you take a look at that! We live in a society. This society, however, survives on several factors, though one overarching one is the atmosphere itself - without it, who knows how much radiation we'd be baked in? If you're like me and have watched several dozen mini-documentary youtube videos, you may have heard that the atmosphere is thinner on tall mountaintops, requiring the use of oxygen tanks. Yep, this ties into our chapter, I swear! Though measuring the distance between sea level pressures and pressures at height can seem trivial, notice that there are other bodies of liquid on our blue marble - some denser than others. Let's take the pressure on the mountaintop as $p_1$ and the pressure at sea level as $p_2$and the distances between them be $y_1$ and $y_2$, with a sample of "human" suspended within the fluid (perhaps a skydiver). Note that if the skydiver was a good 5,000 metres tall, the differences in the pressure and the forces acting on the skydiver would be large enough that a good visualisation of them can be produced. Produced it shall be! This is a diagram of all the forces acting on the skydiver. ![[Pasted image 20230827162617.png]] At the distance $p_2$, or the 'base' of the skydiver, there is a normal force that acts against the weight of the fluid (air) and the skydiver's own weight. This is known as the *upthrust*, given usually by $F_2$ in force-body diagrams. To find the upthrust, remember that we can keep air resistance at a zero (until we can't, then society collapses), so that if "Maxwell" is at terminal velocity the upthrust is: $F_{2} = F_{1} + mg$ If we write the component forces out in terms of pressure we can get the expression: $p_{2}A = p_{1}A + \rho Ag(y_{1} - y_{2})$ Note the density $\rho$ is in the equation. This is a generalisation of mass - where $\rho = mV$. Often times, humans are cylindrical in nature, allowing us to generalise their volumes into the surface area $A$ and their heights $y_1 - y_{2}$. Divide by $A$ on both sides: $p_{2} = p_{1} + \rho g(y_{1}-y_{2})$ Now imagine $y_1$ is the place where the atmosphere peters out, where the pressure of the interstellar medium $p_0$ remains and $y_2$ to be a distance $h$ below it ($-h$) with pressure $p$. This gives us a new, improved expression: $p = p_{0} + \rho gh$ This gives us a value for the total (absolute) pressure on the skydiver! Taking the difference between the atmospheric pressure and the total pressure gives us the **gauge pressure**, which in this case is just $\rho gh$. # Examples # What's Next? Very quick basics' doc. Let's move on to [[Fluid Principles (Mechanics)]]