A flow is classified as being compressible or incompressible depending on the level of variation of density during flow. Incompressibility is an approximation and a flow is said to be incompressible if the density remains nearly constant throughout. The densities of liquids are essentially constant at a particular temperature and thus the flow of liquids is typically incompressible. So liquids are often referred to as incompressible fluids.
Fluid and flow are two different things and hence the question may be framed in a better way than its present form.
The compressibility of a fluid is a measure of the relative volume change in response to a pressure change. It is defined regardless of whether or not this fluid is flowing since it is a thermodynamic characteristic of that fluid.
On the other hand, the compressibility of a flow is directly related to the value of the Mach number in the flow. One can show that second order taylor decomposition of the momentum equation leads to a term for fluctuating pressure that scales as M2. As a consequence, one can consider that the flow is incompressible as long as the Mach number is lower than 0.3 regardless of the fluid at hand. In the case M=0.3, the "acoustic" fluctuating pressure (which is how is often called this second order term in pressure) correspond to 10% of the convective (or aerodynamic) pressure term. To explore further this link please have a look at the derivation of the Low-Mach Number Navier Stokes equation derivation.
Best!
incompressible fluid is a material property:
the density of the fluid is constant.
incopressible flow describes a flow property:
in an incompressible flow the density of a fluid element does not change along its pathline (i.e. the material derivative of the density must vanish)
so you can have an incompressible flow of a compressible fluid (as alexis explains) in the case of low mach numbers or in stratified flows.
an incompressible fluid always results in an incompressible flow
Both are approximations as no fluid is actually incompressible and therefore no flow is exactly incompressible. The accuracy of the approximation depends on the magnitude of the pressure force applied and the compressibility of the fluid. For example air has a high compressibility however for flows with Mach numbers less than about 0.3 the pressure forces are sufficiently small that the air density doesn't change and hence the flow is incompressible. Water on the other hand has a low compressibility and therefore normally water flows are incompressible. Compressibility effects only occur when very high pressures are exerted e.g. water hammer.
Incompressible Fluid = rho=cte (Constant density property)
Incompressible Flow = nabla.v=0 (Divergence of velocity field nought)
The second is a consequence of the first through the continuity equation.
The velocity field is called eventually ¨solenoidal¨.
Incompressible flow means density variation in fluid flow with pressure increase or decrease is not high and it can be neglected. In this case, the fluid can be compressible, e.g. air flow through a fan. But incompressible fluid relates to the fluid not to the fluid flow, .
An incompressible flow is a statement purely about the velocity field (flow). It says the velocity field is divergence-free (or close enough to that state).
An incompressible fluid is a statement about a material (a particular fluid) and whether it can be squeezed/compressed.
Air is a compressible fluid (because you can compress it) that displays incompressible flow at normal speeds (because the flow field tends to be extremely close to divergence-free).
Rubber is an incompressible material, but not a fluid - and therefore never has an incompressible flow associated with it.
Compressibility is a physical property of the fluid, and is implicitly related to fluid flow. For exemple we said that air with a Mach bellow 0.3 is considered as incompressible (air as fluid not as flow), but above this value it should be considered as compressible.
All of the answers were good but I suggest reading the chapter 2 (properties of fluid) and the first pages of chapter 10 (compressible flow) of Fluid mechanics of Cengel. It should be well explained. Just wanted to introduce a very good reference.
The question is inappropriately posed. In any case Alexis' answer is appropriate
Increasing the pressure on an incompressible fluid produces zero volume (or density) change. That is, the the partial derivative of volume (V) by pressure (p) is zero. This is a property of the fluid (not the flow) and is applicable for hydrostatics (zero velocity) as well as hydrodynamics (fluid motion). The fluid compressibility is related to the speed-of-sound (c) which becomes infinite in an incompressible fluid. That is, a pressure change is felt throughout the domain instantaneously. Note that incompressibility is an approximation: all fluids are compressible and have finite c. But, it's a good approximation for many hydrostatic and hydrodynamic scenarios.
We often model flows as incompressible in low-speed aerodynamics or other fluid dynamics conditions (generally with liquids). The common assumption is that the density is constant. This is another way of saying that the fluid is incompressible and that c is infinite (and Mach number is zero). Constant density leads to zero velocity divergence (look at the mass conservation equation of the Navier-Stokes equations). But, zero divergence is an assumption of the flow, not the fluid itself. An incompressible fluid leads to an incompressible flow but not the other way around: velocity divergence is always zero under hydrostatic conditions, even for a compressible fluid. And, we can have incompressible flows with variable density (e.g., low Mach number combustion has variable temperature and density).
Good point. Any incompressible fluid (rho=constant) shows divergence zero (nabla.v=0). The opposite is not true. Infinite sound speed implies ¨simultaneity¨. Which is impossible. The incompressible fluid is a mathematical assumption but is not reality. Divergenceless velocities do not implies incompressibility. See:
https://www.academia.edu/12824552/Relativity_in_The_Tetra-Dimensional_Continuum
The sound speed difuses. The equilibrium is guaranteed. Any fluid is compressible. Otherwise the sound would not exist. Incompressible (rho=constant) fluid is an assumption to simplify the equations, but in this case, forget sound speed. It is meaningless. It is like rigid body (sound speed is also infinite for this). It is a mathematical scheme.
The term "incompressible fluid" is not so precise. It is used, in a generalized manner, to emphasize constancy of density within known physical constraints.
The term "incompressible flow", on the other hand, is a meaningful description of the fluid's variability of density at certain flow conditions, such as pressure , velocity and temperature. In that sense, the same fluid may be described as compressible or incompressible dependingo on the relevant flow conditions.
Stone is close, but Wu is not. An incompressible fluid does not change its volume when subjected to changes in pressure. For an incompressible flow, the divergence of the velocity vector is zero. This is NOT because the fluid density is constant. Indeed, density perturbations (heterogeneities) are both allowed and advected by the fluid flow. This is important in, for example, the Bernard problem of convective instability: the effect of density perturbations caused by temperature gradients (rather than pressure) drive the fluid into motion. The thermal buoyancy is retained in the momentum equation, while motions corresponding to the compression and rarefaction of sound waves, which would quickly radiate away, are not of interest and are filtered out by considering incompressible flow.
The incompressible "div v = 0" flow approximation is used to 'filter out' sound waves from solutions of the mass, momentum and energy transport equations that describe the fluid flow. This quasi-steady approximation is used to describe slow flow: the the Mach number is so small it is treated as if zero; the speed of sound is so much faster than the flow speed, it is treated as effectively infinite; features of fluid flow that would involve acoustic modes are in effect omitted -- in part because their energy radiates away almost instantaneously.
Incompressible flow can be used to model slow flow of a compressible fluid. When the vertical extent of a compressible fluid or gas nears or exceeds its density scale height, however, sub--acoustic effects of bulk compressibility should be retained in the transport equations. These are typically needed within planetary atmospheres and self-gravitating fluids planets and stars. To do so, use the an-elastic approximation. This still filters out fast acoustic modes, but unlike a fully incompressible treatment, it does not require the fluid to passively advect the vertical density stratification. Rising fluid is allowed to expand and sinking fluid is allowed to compress (often adiabatically) and so adapt to, rather than overturn, the ambient density stratification.
One analog to incompressible flow approximation is magnetohydrodynamics. This electromagnetically quasi-steady approximation filters out light waves from solutions of the transport equations, which now include the magnetic transport (induction) equation. The speed of light is in effect treated as if infinite. The divergence of the electric current density (J) is treated as if zero. Curiously, the Maxwell displacement current is in effect omitted from the "pre-Maxwell" equations of MHD, which are usually reduced to the magnetic induction equation. In MHD, motions are slow compared to light speed, the Lorentz transformation of special relativity reduces to the Galilean invariance of everyday life, and the energy of a particle amounts to its Newtonian kinetic energy.
Incompressible flow does not mean that the density is constant. If the ratio of change in density to density is less than 5%, the flow can be considered as incompressible. The corresponding Mach number would be around 0.3. This is usually assumed to minimize the mathematical complexity for solving fluid flow problems.
In incompressible fluid, the density is assumed to be constant with change in pressure. However air or even water is compressible at high pressure (20000 bar!). Again some threshold limit is given up to which one can consider a certain fluid to be incompressible.
Small density changes (better called low Mach number) flows are still a subset of incompressible flows. Two liquids that do not mix (like oil and water) and flow together in complex ways (like oil in an undersea pipeline always does) can have an arbitrary different density differences in the flow (much larger than 5%) and still be fully incompressible (Mach number essentially zero).
An incompressible flow is best defined as a flow where the divergence of the velocity is zero or negligible (compared to the other physical inverse timescales). It is best to leave density or its variation out of the definition since these only lead to certain subsets of the actual situation.
Dear all:
I have a similar question to this topic: I have a nanoparticle filled suspension which flows by a filtration medium, which means the particle would be deep bed filtrated by the medium along the flow length. So this is my assumption: the fluid is not incompressible, as the density changes along the flow length, the flow itself I think is also not incompressible, as the density of the defferencial volume changes. But strangely I found several papers in which mostly such a case is assumpted as incompressible flow which is right now rather disturbing me. But by another thought, ot couldn't be that in such a case just the fluid itself without the particle is considered right? if that's the case then of course the fluid itself is incompressible? Maybe has someone experience on this topic? thanks in advance!
Solids and liquids are essentially incompressible and combinations of them are as well.. Variable density, which you have, has nothing to do with whether that material can be compressed or not.
So water and oil mixed together are incompressible even though the density depends on if you are in the water or oil.
Salt water and freshwater mixed together are incompressible. This is like your case. Chlorine and Sodium are charged nanoparticles. Even though the density can vary all over the fluid (depending on how salty it is).
A constant density fluid is clearly also incompressible.
But this does NOT imply the converse. All variable density materials are NOT compressible. Constant density is a subset of all possible incompressible materials.
Mr. Dilmurat Abliz you are dealing with two materials model, also called two fluid model when both are fluids. Volume fraction may vary in space and time but components are incompresible, also the equations related (each phase) are treated as incompressible. i.e. solenoidal fields of velocities.
Incompressible flow refers to a flow in which the material density is constant within a fluid parcel that moves with the flow velocity. Incompressible flow does not imply that the fluid itself is incompressible. Even compressible fluids can – to good approximation – be modelled as an incompressible flow. Incompressible fluids have constant density irrespective of flow consideration.
Incompressible fluid is a material that has a constant density with pressure change. so at constant T we have: (∂ρ⁄∂P)=0
But an icompressible flow is a flow that its Ma number is lower than 0.3. It means inertia force should be lower than elastic force. and also it means we can Regardless density changing in front of first value of density.
A fluid is said to be incompressible when density remain constant with respect to pressure.
A fluid flow can be treated as incompressible flow if Mach number is less than 0.3.
The limit 0.3 for Mach number is only for standard air. If you change the isoentropic exponent of the gas, you change the limit.
For the incompressible flow Divergence = 0 [ie.volumetric dilation rate is zero]
For the incompressible fluid density = constant
Compressible flow : The change in density of the fluid is more than 5 percentage, then the fluid flow is considered as compressible. Generally in Aerodynamics, fluid flow greater than Mach 0.3 is considered as compressible.
Incompressible flow : The change in density of the fluid is less than 5 percentage or negligibly small, is considered as incompressible. Generally in Aerodynamics, fluid flow less than Mach 0.3 is considered as incompressible.
From most of the above answers, it seems that M = 0.3 is a magic boundary between compressibility and incompressibility .
This is true only if the flow is adiabatic and anergodic, so isoenergetic (no heat, no work added to the fluid), and isoentropic.
People are forgetting that ρ = ρ(p,T).
Let us simply have air that enters a heat exchanger at M = 0.01 and Tin = 300K and exits at Tout = 600K. Is the flow through the exchanger incompressible or not ???
Regards
The M=0.3 boundary is no magic!
It comes from the Taylor series expansion of the Navier Stokes equation with respect to the pressure perturbation.
In the case where M
Of course there will be pressure drops in the flows you are mentioning, but the pressure drop is related to the conservation of the mass flow rate in stationary flows. Boundary layers and singularities such as sudden changes in cross flow area will necessitate a negative pressure gradient in the direction of the flow to maintain the mass flow rate. This goes also this an increase of the entropy as it reflects the irreversibilities in flow.
Yet, this pressure change is essentially stationary and does not influence the density as long as M
You are right, I should have completed my first answer with second one before hitting the send button. When I said it would be unaffected, I was thinking only of the compressible part of the pressure.
I can reassure you. Nature behaves the same here ;-)
Best.
In compressible fluid is the fluid when compressed its volume will not be changed meaning its density is independent of pressure. Also, in-compressible flow means that the volume of the flowing fluid will not altered by compression which means also invariant density of the fluid with pressure during the flow.
Best wishes
"Incompressible fluid" is a terminology for denoting an intrinsic nature of a fluid to not change his volume under the action of normal stress. We could also debate if it exists in nature a fluid (or a liquid) that has exactly zero change in the volume (the measure of volume change being the divergence of the velocity field).
More interesting is "incompressible flow" that is nothing else that a model we adopt under circumstances that allows a compressible fluid to produce a dynamics "resembling" that of an incompressible fluid. This model requires physical hypotheses to be fulfilled and has mathematical implications in the resulting simplified set of equations. Note that the divergence-free contraint (zero change in the volume of the fluid) on the velocity field simply ensures that the density is constant along a path-line not that does not change in time and space.
Starting with the total derivative expression that is the most familiar from multivariable calculus: dn/dt=del n/del t +del n/del x (dx/dt)+del n/del y (dy/dt)+del n/del z (dz/dt), or expressed in vector form of dn/dt=del n/del t +(v dot Grad)n, where the gradient operator Grad = del /del x i+del/ del y j+ del/del z k. Since Grad(nv)=(v dot Grad)n+nDiv v, for divergenceless or incompressible (non-deformable) flow, Div v=0, then dn/dt=del n/del t + Grad nv, and since J=nv is the flux vector (in number of particles flowing per unit time through a unit cross-sectional area), one has the continuity equation dn/dt=del n/del t +Div J. Note dn/dt is the rate of generation.
Ans:
Definition: Incompressible fluids are those fluids whose density is independent of pressure. On the other hand, the flow of a fluid is said to be incompressible if the density of the fluid remains almost constant throughout. That is, ρ = constant
The flow of compressible fluid is not necessarily compressible as the density of a compressible fluid may still remain constant during flow.
When fractional change in volume of a fluid is negligible, even after large pressure applied (external) on the fluid, is know as incompressible fluid. It is a fluid property.
When fluid is flowing and it's density does't change during the flow even fluid is compressible in nature, then flow is called incompressible. It's is a flow property, it's depends on pressure, velocity and temperature. It's is more important in flow of air or any gas.
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