# What is Compressible: Definition and 79 Discussions

In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility or, if the temperature is held constant, the isothermal compressibility) is a measure of the relative volume change of a fluid or solid as a response to a pressure (or mean stress) change. In its simple form, the compressibility

κ

{\displaystyle \kappa }
(denoted β in some fields) may be expressed as

κ
=

1
V

V

p

{\displaystyle \kappa =-{\frac {1}{V}}{\frac {\partial V}{\partial p}}}
,where V is volume and p is pressure. The choice to define compressibility as the negative of the fraction makes compressibility positive in the (usual) case that an increase in pressure induces a reduction in volume. The reciprocal of compressibility at fixed temperature is called the isothermal bulk modulus.

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1. ### Pressure drop through volumes of compressible fluid

Thanks for your response. I'm trying to estimate the pressure in the cavity, i.e. P2. I know the areas, A1 which in practicality is an annulus and A2 which is a 600m pipe with i/d 8mm. I would like to initially understand how to calculate the pressure drop across the annulus. At the moment I'm...

21. ### Simple compressible system and flow system

I would like to ask about the difference between the simple compressible system and the flow systems. "In the absence of such effects as magnetic, electric, and surface tension, a system is called a simple compressible system. The total energy of a simple compressible system consists of three...
22. ### Pressure drop across a tube section - compressible flow

So, a coworker approached me today with a 'simple problem' to solve, looking to sanity-check a design choice. Much to my dismay, I had no idea how to approach it. Worse, google had no straight-forward answers either, and any formulae I did find seemed circular. This seems too simple to...
23. ### A How to Solve Isothermal Incompressible Navier-Stokes for Compressible Fluid?

I did a lot of googling but could not find a satisfying answer to my question, hence a post here. Question: How to solve (or close) the isothermal incompressible Navier-Stokes equations for an isothermal compressible fluid? Situation: We have a compressible fluid, for example a gas. The flow...
24. ### Compressible air flow from a tank through a regulator

This is probably a simple question but I am really struggling as to where to start. We have a tank of compressed air, Volume of tank (V1) = 0.2litres Pressure of tank (P1) = 206.8 bar Regulator Pressure (P2) = 58.6 bar I would like to find the volume of air that can pass through the regulator...
25. ### I Does Space Compressibility Affect the Big Bang?

I was asking some Big Bang related question on Reddit and someone replied "The big bang is an explosion of space itself. A shock wave requires an explosion propagating into pre-existing material. Not only was there no pre-existing material, there was no pre-existing space to hold it. This all...
26. ### Pressure on Piston due to Compressible flow

is it correct modeling mathematical model for Compressed air engine, As here air Flowing through Pipe in Kg/s and its not a continuous flow and flow through vent into the cylinder and pushes Piston and and Piston moves down. As I created model like this (P1*V1)^Y = (P2*V2)^Y So, P2 =...
27. ### Nozzle/Diffuser equation for compressible flow

I was reading a bit about comrpessible flow and I came upon a problem, there's a diffuser which has air at Ma=0.9 at its inlet and the air comes out at 0.65, how should I go about finding the ratio of the inlet and outlet areas? I know It's related to this equation but I'm unsure about how...
28. ### Pressure calculation for compressible gas and variable 'g'

I have what seems like a straight forward question, but am unable to find a formula. The question originates from my previous topic which was trolled: https://www.physicsforums.com/threads/blowing-up-a-balloon-using-centrifugal-force.848892/ Basically I have a 1.5m hollow length of 10mm tube...
29. ### Newtonian fluid in compressible flow?

When compressible effects are accounted for, viscosity should vary with temperature. Doesn't this violate the concept of Newtonian fluids, where shear stress is linearly proportional to the strain rate?
30. ### Solving 3D Compressible NS for Cylindrical Pipe

Can somebody provide a solution for this question? convert 3 dimensional unsteady compressible NS equations to axisymmetric 2 dimensional incompressible laminar form for a cylindrical pipe, then make a derivation of streamwise velocity profile u(r) using the appropriate boundary conds. thanks
31. ### Fluid Dynamics: Static pressure in compressible Liquids

Homework Statement [/B] "Derive a relation between the static pressure P at a point and its depth y from the free surface of the liquid. Given the surface density of liquid is ρο, and compressibility of the liquid is k." Homework Equations ##ρ(P) = ρ_οe^{kP}## ##dP = ρg dy## The Attempt at a...
32. ### Compressible fluid other than air.

Hello Is there any fluid other than air which is compressible. http://www.scienceinfusion.com/air-the-fluid/
33. ### Navier-Stokes Equations for a Compressible Fluid

Hello, I don't know if this question belonged here or in General Physics, so I apologize if I made a mistake. My question is simple, what are the Navier-Stokes Equations for a Compressible Fluid? I don't mean from a conceptual point of view, what I mean are the mathematical equations themselves...
34. ### Calculating Pressure Loss in Compressible Fluid Flow: A Case Study

I have a quick question regarding compressible fluid flow, specifically: for a given amount of time, how much pressure is lost when attaching a balloon valve to a small air tank. I decided to model my solution after the following problem (from an old fluid mechanics textbook of mine), Air is...
35. ### Choked flow out of air compressor and wind tunnels

I posted this on Eng-tips and no replies yet:( I'm trying to design an as-simple-and-cheap-as-possible supersonic wind tunnel using an air compressor (this even possible? given the energy losses from shock waves...). I have access to a Porter-Cable 150psi, .8hp air compressor. Questions: 1...
36. ### Understanding Compressible Shock Waves: Exploring Theta, Beta, and Mach Curves

Hi all, I have some prob to undestand the shock wave in compressible flow, more precisely the "theta, beta, Mach curve) - Why when "theta" exceeds theta (max) there is no oblique shock? (how we can explain this physicaly)? - What is the difference betwwen weak shock and strong shock? - why in...
37. ### Compressible Flow, Pressure and Mass Flowrate

I am doing a lab report and it is to do with compressible flow through rotameters. An upstream and downstream rotameter to measure flow rate with a needle valve between the two. The needle valve acts as a fixed orifice in one part of the experiment. Then the inlet pressure is altered. Plotting...
38. ### Mass flow rate for compressible flow

I am confused about the relation of mass flow rate with different mach numbers in a compressible flow. In wikipedia (http://en.wikipedia.org/wiki/Choked_flow), I read the following: "Although the gas velocity reaches a maximum and becomes choked, the mass flow rate is not choked. The mass flow...
39. ### TI89 calculator solver in functions?

I was wondering if it's possible to use the TI89 Titanium's built-in solver with programs. More specifically, for compressible flow problems, I'd like to calculate mach number based on area ratio, specify whether the flow is subsonic or supersonic, then do something with the corresponding...
40. ### How to size an orifice on a vent line

I would like to install a vent stone on a 3/4" vent line. The line vents upwards of 1500 psig of stored gasous nitrogen in under 1 second. The vent stones are only rated for 300 psig, so I'd like to add an orifice just upstream to limit the exit flow rate to a point where it can handle the...
41. ### Compressible vs. incompressible substance

I'm confused about which phases are considered compressible and which are considered non-compressible. In classical thermodynamics, gases and liquids are considered compressible. This is what the state principle (2 independent properties define all other properties) applies to gases and...
42. ### Help with compressible flow problems

Homework Statement Calculate the pressure increment required to isentropically compress air and water at 1 atm and 20°C to 50% of their volume. The isentropic bulk modulus for water at 20°C is 2.24 109 N/m2, and air can be considered an ideal gas with γ =1.4 . Homework Equations...
43. ### Pressure and density of compressible fluids.

If a fluid is compressible, will the density be directly proportional to the pressure? (I'm sure there's a limit where an increase in pressure stops producing a change in density, but I'm talking about for more "normal" (smaller) amounts of pressure.)
44. ### Determination of density at a depth in a compressible fluid.

Determination of density at a depth in a compressible liquid. Hi all, Let us consider a tank containing some compressible liquid with bulk modulus K and having density at its surface s. Consider some part of liquid with volume V, a depth h below the surface. Due to liquid above it there...
45. ### Compressible fluid through a narrow tube.

Homework Statement For a flow of a compressible fluid through a narrow tube, the following statement is correct a) the volume of the fluid crossing any section of the tube is constant. b) density of the fluid is independent of pressure. c) mass of the fluid crossing any section of the...
46. ### The paradox of Hawking radiation - is matter infinitely compressible?

The hypothetical Hawking radiation means that a set of baryons can be finally transformed, "evaporate" into a massless radiation - that baryons can be destroyed. It requires that this matter was initially compressed into a black hole. If baryons can be destroyed in such extreme conditions, the...
47. ### Compressible flow problem in heated tube reactor

Hey y'all, Thanks in advance for any help on this. I'm kind of stumped by this problem I've come across in the lab. We have a tube reactor with a nozzle, and we want to measure the combustion/pyrolysis products coming out the model using GC/MS and MBMS. Right now, we are just running...
48. ### Fluid Mechanics: Compressible Fluids, density function

Homework Statement "Suppose that a liquid has an appreciable compressibility. Its density therefore varies with depth and pressure. The density at the surface is ρ0 (a) Show that the density varies with pressure according to ρ=ρ0ekp where P is gauge pressure at any depth and k is the...
49. ### Compressible flow in cylindrical coordinate

Hi, could anyone tell me a reference on Navier-Stokes equation for the COMPRESSIBLE flow in CYLINDRICAL coordinate? Just can't find a good reference book. Thanks in advance. Jo
50. ### VBA Excel Functions for Compressible Flow. Houghton and Brock Tables

G'day! This is my first post on this forum and I hope you find it usefull! Attached are complete set of Excel functions for *Isentropic Flow *Prandlt Meyer Expansion *Raleigh Flow *Fanno Flow *Plane Normal Shock *Plane Oblique Shock They are contained in the attached workbook (zipped as it...