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


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





{\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. N

    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...
  2. JD_PM

    A Cavitation: radius of a bubble for compressible flow

    The liquid-vapor mass transfer (evaporation and condensation) is governed by the vapor transport equation: $$\frac{\partial}{\partial t} (\alpha_l \rho) + \nabla \cdot (\alpha_l \rho \vec v) = \dot m^{+} + \dot m^{-}$$ In the incompressible flow case (constant density), it reduces to $$...
  3. S

    Engineering Calculating valve sizes for a compressible liquid

    I have converted given pressures from bar gauge to bar abs Inlet pressure = 20 - 1.013 = 21.013 bar abs Outlet pressure = 6 + 1.013 = 7.013 bar abs therefore pressure drop (x) x = {p_1 -p_2 \over p_1 } = {21.013 - 7.013 \over 21.013} = 0.6662542236 bar abs Comparing to the chart values for...
  4. stuartsjg

    I Compressible choked gas flow through an orifice -- Excel formula

    Hello, I normally get these things working but I am a bit stuck as i don't feel I am getting sensible answers... The problem is simple (!): Q: Model the flow through an orifice with an upstream/supply pressure of 301BarA where the downstream pressure is in the range 1BarA to 301BarA. The...
  5. C

    Most compressible volumes: synthetic fibre versus natural eider down?

    I'm just purchasing some exped kit including coats and sleeping bags containing down as the insulator. The key superlative of down is that it can be compressed and then recovers to a big volume. If one ounce of material re-expands, after compression, to 800 cubic inches then this is called '800...
  6. D

    Tubing Pressure drops with Compressible Fluids

    I am a poor, dumb EE often stuck with the odd plumbing calculation. I am often asked questions like: "what size tubing do I need to convey 10 SLPM of 20 PSIG oxygen 200' with no more than 2 PSI pressure drop?" I generally treat the fluid as in-compressible and use Darcy-Weisbach (I like Bellos...
  7. P

    What is the method for calculating the angle Θu in compressible flow?

    Hello good people! I'm studying the compressible flow and the book refers to this example. I can't understand how does it calculate the angle Θu? In the previous example, there is a method to calculate it but it requires all the properties once the fluid is deflected, therefore, that's not the...
  8. rjomega

    Effect on Volume of a Change in the Pressure of Compressible Gas

    Will the available Volume of oxygen gas for use of patients increase when the pressure decreases from 12.4 MPa to 500 KPa? Is using boyle's law the right way to calculate the available volume?
  9. Twigg

    A Adiabatic Compressible Flow in a Converging Duct

    For compressible flow in a duct, mass conservation combined with reversibility (no entropy change) implies $$(1-\frac{u^2}{c^2})\frac{du}{u} = -\frac{dA}{A}$$ where u is the flow velocity of the gas, c is the speed of sound in the gas, and A is the area of the duct. I am assuming a calorically...
  10. YoungPhysicist

    B Is Any Material Truly Incompressible Under Special Relativity?

    I thought that if something is incompressible, then when we push on this thing, the other end of it will move instantly, which is a kind of FTL information transport and is impossible. So does that mean literally everything, including atom nucleus or even some elementary particles(if they can be...
  11. B

    A What property of air makes it compressible?

    What would you change about air to make it have the same density at sea level but the atmosphere would only be a few miles high instead of a several hundred miles high? I am a high school physics teacher. As I ponder this possibility, my first thought is I could increase the strength of the...
  12. I

    Measuring Pressure For Compressible Fluid Systems?

    Is measuring pressure for a compressible fluid system angle dependent?For a compressible fluid, Bernoulli's Law gives us a relation between two points along a closed system. More specifically it gives us the relation between two cross sections belonging to two distinct points in the closed...
  13. S

    B How can I model a density function of a compressible fluid?

    I have a cylinder of some dimensions. I have a compressible liquid inside. Assuming a constant temperature, no atmosphere, no convection currents within, because it is in a cylinder, there will be no variations in density horizontally (the fluid will have time to settle). Now because there is...
  14. U

    Compressible flow or incompressible flow equation?

    Hello everyone.. I am using 2-dimension Navier Stokes equation, but I confused that my problem is compressible or incompressible flow form, because if I have initial pressure and temperature and velocity for x-axis only in one grid that they are so very high but the others grid are zero. Can I...
  15. O

    FAVRE-average: Compressible or just varying density

    Hi. I am modelling a fluid flow that is incompressible and has variable density. I am applying RANS turbulence models. When deriving the equations for the mean flow when the denisity is non-constant using the Reynolds average, I do not get the same as the standard RANS-equations. This even if I...
  16. N

    Threshhold compressible flow Ma = 0.3

    Hi guys, I'm trying to delve into compressible flow and in the various textbooks I'm reading I've found two school of thoughts when it comes to how to calculate the threshold (or error compared to incompressible flow) of 'M' when to consider a flow compressible. In Fundamentals of Aerdnyamics...
  17. Davidkippy

    Should Aerodynamics Fundamentals Precede Compressible Aerodynamics?

    I'm going to be an aerospace/mechanical engineering student at UAH next year and I am coming up with my four year plan. Two courses, "fundamentals of aerodynamics" and "compressible aerodynamics", are not prerequisites for each other, and they are both required. Based on your experience with...
  18. Perodamh

    Which gas is more compressible

    Homework Statement Gas A at 125KPa (abs) is compressed isothermally and gas B at 100kPa(abs) is compressed isentropically (Y = 1.4). Which gas is more compressible?[/B]Homework Equations Compressibilty = 1/bulk's modulus Bulk's modulus = F/A/V/v or volume stress/volume strain The Attempt at...
  19. B

    Momentum Equation for compressible 1D flow

    Homework Statement Derive the differential momentum equation: dp=-\rho udu. Homework Equations \oint_{ CS}^{ } \rho \vec{U}(\vec{U}\cdot \vec{n})dA=-\oint_{ CS}^{ } p\vec{n}dA for steady state flow... The Attempt at a Solution I tried to solve it like in the attached picture, but can someone...
  20. F

    Compressible inviscid vorticity convection w Rankine Vortex

    Homework Statement The compressible inviscid vorticity convection equation: $$\frac{D(\frac{w}{\rho})}{Dt}=(\frac{w}{\rho})\cdot \nabla U + \frac{1}{\rho}\nabla P \times \nabla (\frac{1}{\rho})$$ differs from the incompressible version in two important ways : 1) The convected quantity is...
  21. M

    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. C

    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. M

    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. G

    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. Puma

    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. C

    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. DanielSauza

    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. O

    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. C

    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. P

    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. F

    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. A

    Compressible fluid other than air.

    Hello Is there any fluid other than air which is compressible. http://www.scienceinfusion.com/air-the-fluid/
  33. P

    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. P

    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. yangshi

    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. S

    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. C

    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. L

    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. J

    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. steves1080

    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. G

    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. T

    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. Nathanael

    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. O

    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. J

    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. J

    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. G

    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. R

    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. J

    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. M

    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...