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let \rho is density of phase fluid and v is velocity of phase fluid (velocity in a phase space!!)

we take the equation of continuity (we suppose "mass" of phase fluid is conserved) and using Hamilton equations (we suppose classical mechanical system)

[ dot{p_i} = -frac{partial H}{q_i} ]

[ dot{q_i} = +frac{partial H}{p_i} ]

we obtain the result

[ frac{mathrm{d}rho}{mathrm{d}t} = - rho,mathrm{div},v = -rho sum_i left( frac{partialdot{q_i}}{q_i} + frac{partialdot{p_i}}{p_i} right) = 0 ] let \rho is density of phase fluid and v is velocity of phase fluid (velocity in a phase space!!)

we take the equation of continuity (we suppose "mass" of phase fluid is conserved) and using Hamilton equations (we suppose classical mechanical system)

\[ \dot{p_i} = -\frac{\partial H}{q_i} \]

\[ \dot{q_i} = +\frac{\partial H}{p_i} \] we obtain the result

\[ \frac{\mathrm{d}\rho}{\mathrm{d}t} = - \rho\,\mathrm{div}\,v = -\rho \sum_i \left( \frac{\partial\dot{q_i}}{q_i} + \frac{\partial\dot{p_i}}{p_i} \right) = 0 \]

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Is blood a compressible fluid?

if the density of the fluid changes with respect to pressure is called compressible fluid f the density of the fluid does not changes with respect to pressure is called incompressible fluid


What is the difference between Co2 compressible and Co2 incompressible?

Gasses are compressible and liquids and solids are incompressible. Using this information one can surmise that CO2 compressible would be the gas phase of CO2 and CO2 incompressible would be the solid (dry ice) phase of CO2.


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In incompressible fluid density is same because velocity gradient is same on every layer of liquid at any cross section.


Water is incompressible fluid when what we do for bring it is compressible?

It can't be made compressible, if that's what you mean - unless you turn it into steam.There really is no such thing as an incompressible fluid; but the amount a liquid's volume changes under pressure is so little, that for many practical purposes it can be considered incompressible.


When are fluids useful when they are incompressible?

Fluids are useful when they are incompressible when they need to maintain a constant volume while transferring forces or energy. In applications such as hydraulic systems, incompressible fluids are advantageous because they allow for precise control and transmission of pressure without significant volume changes. Additionally, in engineering designs that require stable and predictable fluid behavior, incompressible fluids are preferred to ensure consistent performance.

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Why does the density of an incompressible fluid remains constant?

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What is the definition of incompressible flow and how does it relate to fluid dynamics?

Incompressible flow is a type of fluid flow where the density of the fluid remains constant. In fluid dynamics, this concept is important because it simplifies the equations used to describe the behavior of the fluid. By assuming the fluid is incompressible, engineers and scientists can more easily analyze and predict the flow of fluids in various systems, such as in pipes, channels, and around objects.


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Why does incompressible fluid happen?

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Water is incompressible fluid when what we do for bring it is compressible?

It can't be made compressible, if that's what you mean - unless you turn it into steam.There really is no such thing as an incompressible fluid; but the amount a liquid's volume changes under pressure is so little, that for many practical purposes it can be considered incompressible.