# What is Incompressible flow: Definition and 23 Discussions

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. ### A Why are the Navier-Stokes equations inconsistent in this case?

Consider the case of a one-dimensional incompressible, non-viscous fluid flowing down a vertical pipe under the influence of gravity. Since we assume the flow is constant along the cross section of the pipe from the one dimensional assumption, let us denote the velocity of the fluid down the...
2. ### I Boundary Conditions For Modelling of a Fluid Using Euler's Equations

Hi! I want to use Euler's equations to model a 2 dimensional, incompressible, non-viscous fluid under steady flow (essentially the simplest case I can think of). I'm trying to use the finite difference method and convert the differential equations into matrices to be solved using MATLAB. I set...
3. ### Unsteady flow of water being discharged from a tank

I am currently modeling the altitude that a water rocket can attain. In order to do this i am first modeling the the thrust phase. Due to the water mass decreasing with time (the same goes for the pressure - it decreases over time as the water is expelled out of the nozzle). This is an...
4. ### 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...
5. ### Modeling a multiple inlet piping system

Hello, PF! I’m trying to model a real piping system, which has multiple inlets and one outlet, so I can’t use Bernoulli’s equation. Instead, I’m planning to use the generalized macroscopic energy balances as shown in BSL, which allow for any number of inlets and outlets. However, first I want...
6. ### I Why incompressible flow does not satisfy energy equation?

I encountered this statement on my lecture notes today, I don't understand why compressible flow needs to have another constraint of energy equation while incompressible flow only satisfies continuity and momentum equation. And how is this energy equation related to the speed of sound?
7. ### 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...
8. ### I Spectral representation of an incompressible flow

Hi PH. Let ##u_i(\mathbf{x},t)## be the velocity field in a periodic box of linear size ##2\pi##. The spectral representation of ##u_i(\mathbf{x},t)## is then $$u_i(\mathbf{x},t) = \sum_{\mathbf{k}\in\mathbb{Z}^3}\hat{u}_i(\mathbf{k},t)e^{\iota k_jx_j}$$ where ι denotes the usual imaginary...
9. ### Modeling ideal gas flow using Bernoulli's equation

Hello, PF! I'm currently brushing up my fluid mechanics and came across some questions while studying the compressible flow of an ideal gas using Bernoulli's equation. First, consider incompressible flow in the following system Neglecting any changes in elevation, the Bernoulli equation for...
10. ### Boundary layer equations for incompressible flow

Hello everyone. I posted this question in another forum and got no answers so I'll try and re-post it question here. I need to deliver a correct answer to the cited question below to my course responsible teacher. Below is also my own solution and thoughts on the problem but I don't know if I am...
11. ### Boundary layer equations for incompressible flow

Hi. I am new here so I please let me know if I should post this in another forum. I have been struggling for a while with the following homework problem: "State the boundary layer equations for incompressible flow over a solid, weakly curved boundary of a Newtonian fluid. What approximations...
12. ### Potential flow, inviscid flow, incompressible flow

I have a couple of questions regarding several key areas of fluid mechanics: 1. My first question deals with the Navier-Stokes equations. Does incompressible&irrotational flow imply inviscid flow? My answer is yes and here is my thought process. In the incompressible form of the Navier-stokes...
13. ### MHB Incompressible Flow: Questions and Answers

Hey! :o In my notes there is the following example: One dimensional incompressible flow in a channel of constant section. $$\overline{u}=(u(x, t), 0) \ \ \ \ \ p(x, y, t)=p(x)$$ incompressible flow: $\partial_x u=0$ Euler equations: $\rho_0 \partial_t u=-\partial_x p$ \Rightarrow...
14. ### Fluid Mechanics: Constant Pressure and Incompressible flow

Assuming a flow can be idealised as incompressible, then can you use the constant pressure assumption ? I just want to get my understanding clear. My problem is the following.Consider a fluid element with volume ##V## and a fixed number of molecules. If the flow is incompressible, then the...
15. ### Incompressible flow in a funnel

I am having a few issues reconciling Bernoulli's principle and the continuity equation for an incompressible flow in a horizontal funnel where there is significant difference in the area from the start to the end. More specifically, I want to work out exactly what the fluid is doing once it...
16. ### Fluid Mechanics: Incompressible flow and pressure

Most liquids can be assumed to be incompressible, since the Mach-number is much smaller than 1. That means that the density variations are negligible and from the relation between pressure p and density ρ, p=c_s^2 \rho we see that the pressure in constant as well. Now, say that I look at a...
17. ### Low Mach Numbers: Incompressible flow or fluid

Hi When we talk about a fluid moving at low Mach numbers, it is said to be incompressible. But does this mean that the flow is incompressible (i.e., material derivate is zero) or does it imply that the fluid itself is incompressible (constant density)? If anybody has a reference (book...
18. ### Compressible vs. Incompressible Flow Equations

As a private study I'm trying to figure out fluid dynamics applied to compressed air systems. Most of the material I am studying considers only incompressible fluid flow. From what I understand about the differences between compressible and incompressible flow in terms of the equations it only...
19. ### (HELP )Compressible vs incompressible flow (QUESTION)

(HELP PLZ)Compressible vs incompressible flow!(QUESTION) Ok! I think I know the difference between the two, which is basically the density. My question is actually when is the equation of properties like (Static temperature, Total temperature, Total pressure, Static enthalpy, dynamic viscosity...
20. ### 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...
21. ### 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...
22. ### Difference between compressible and incompressible flow

Hi all I am really confused with what is the actual meaning of compressible and incompressible flow?
23. ### 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...