Incompressible Definition and 68 Threads

In fluid mechanics or more generally continuum mechanics, incompressible flow (isochoric flow) refers to a flow in which the material density is constant within a fluid parcel—an infinitesimal volume that moves with the flow velocity. An equivalent statement that implies incompressibility is that the divergence of the flow velocity is zero (see the derivation below, which illustrates why these conditions are equivalent).
Incompressible flow does not imply that the fluid itself is incompressible. It is shown in the derivation below that (under the right conditions) even compressible fluids can – to a good approximation – be modelled as an incompressible flow. Incompressible flow implies that the density remains constant within a parcel of fluid that moves with the flow velocity.

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  1. C

    Solving Incompressible Flow Homework: Find f(r)

    Homework Statement A velocity field is given by \vec {u} = f(r)\vec{x}, r = | \vec{x}| = \sqrt {x^2 + y^2 + z^2} written in rectangular cartesian coordinates, where f(r) is a scalar function. Find the most general form of f(r) so that \vec {u} represents an incompressible flow...
  2. I

    Incompressible strips and edge states?

    I'm reading the paper by D.B. Chklovskii where he quantitatively describes the appearance of strips of incompressible electron fluid in a 2DEG when a magnetic field is applied to it. What I don't get is the relationship between these strips of incompressibility and the edge states in the 2DEG...
  3. K

    Incompressible Navier Stokes - Short Question

    Hello! The incompressible Navier Stokes equation consists of the two equations and Why can't i insert the 2nd one into the first one so that the advection term drops out?! \nabla\cdotv = v\cdot\nabla = 0 => (v\cdot\nabla)\cdotv = 0
  4. Saladsamurai

    Fluid Mechanics'Deriving' Incompressible Flow Criteria

    Here we go... My text attempts to 'derive' an expression that explains when a flow is compressible or not: Great :rolleyes: ... if there's anything I like better than making density approximations, it's playing 'fast and loose' with them. :smile: He then goes on to say: I am...
  5. D

    Compressing an incompressible fluid.

    I was reading the proof of how the work done on an ideal fluid which has been pressurized to a pressure 'P' is P. There I read that the work done will be the product of the area of cross section of the piston, the pressure applied on the piston and the distance moved by the piston. If the...
  6. F

    Cl,0 ; it is how much efficient to calculate Cl,0 (i.e. Cl incompressible)

    Cl,0 ; it is how much efficient to calculate Cl,0 (i.e. Cl incompressible) when the airfoil is thin, symmetrical, at alpha = 3 degrees and moving at low speed. Actuall it appeared in my compressible aerodynamics paper where i ha to calculate CL. I was given Lift per unit span, dynamic head q, in...
  7. B

    Transient inviscid incompressible pipe flow

    Hello I am trying to better understand transient fluid dynamics in pipes. First, I am attempting what I believe should be relatively simple problem. I have a constant area horizontal pipe partially filled with a stationary incompressible inviscid fluid. The part of the pipe that is filled is...
  8. A

    Incompressible viscous liquid questions

    Which of the following is true in a streamlined flow of incompressible viscous liquid? A) When a fluid is in streamlined flow then there is transport of energy from one layer to another. B) The speed of flow at all points in space is necessarily same. C) The velocity of the liquid in contact...
  9. V

    Factors that affect viscosity of incompressible Newtonian fluid?

    What are the factors that affect viscosity of incompressible Newtonian fluid? Here is what I think: Temperature: When we increase the temperature of a fluid (controlled volume) the frequency ofintermoleculer collisions increases. Does this mean viscosity decreases? And if so, does...
  10. M

    Difference between compressible and incompressible flow

    Hi all I am really confused with what is the actual meaning of compressible and incompressible flow?
  11. M

    Difference between incompressible viscous and incompressible inviscid flow.

    The Navier-stokes equations have no definite understanding of how it works; does the incompressible viscous and inviscid flow have a definite understandings (Hannah and Stephens)
  12. B

    Divergence Theorem and Incompressible Fluids

    Homework Statement Hi, I'm trying to follow the proof for the statement \nabla . u = 0 I'm basing it off this paper: http://delivery.acm.org/10.1145/1190000/1185730/p1-bridson.pdf?key1=1185730&key2=4151929021&coll=GUIDE&dl=GUIDE&CFID=25582973&CFTOKEN=82107744 (page 7, 8) In...
  13. P

    Incompressible Fluid simulation - SPH doesn't work

    Incompressible Fluid simulation - SPH doesn't work :( Hello all, I've been stuck in my project: Fluid Simulation using Smoothed Particle Hydrodynamics for a few days now. I do understand the core principle that fluid properties are calculated by integration on kernel W with range h. But...
  14. S

    Is Del . V = 0 a valid assumption for steady flow of water through a pipe?

    a perfect and incompressible fluid flowing in circular path about a center. the flow is two-dimensional and steady. I need to find differential relation between the pressure and the tangential velocity and the radial distance.?? I couldn't find which eqn i can use for this problem. I first...
  15. A

    Derivation of incompressible navier-stokes

    I'm trying to find a simply derivation of the incompressible navier-stokes equations, as stated in the official problem description at the cmi website, or in "The Millenium Problems", by Keith Devlin: \frac{\partial u}{\partial t}+(u\cdot\nabla)u=f-\nabla p+\nu\Delta u \nabla\cdot u=0 I...
  16. Clausius2

    When can one assume Incompressible Flow?

    Incompressible Flow: Assumptions for its validity After a recent hot discussion brought to the board, I think it would be good to clear up this question. Firstly, it does not make sense to talk about an incompressible fluid. There are no incompressible fluids in the Nature, we can only...
  17. A

    Why does div(v)=0 for a fluid means that the fluid is incompressible?

    why does div(v)=0 for a fluid means that the fluid is incompressible?
  18. S

    Specific Heats for Incompressible Fluids

    Given the following equation: Cp = Cv + R Where Cp is specific heat (constant pressure), Cv is specific heat (constant volume), and R is the universal gas constant. However, my book states that for an incompressible fluid, Cp = Cv. How can this be the case given the above equation...
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