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chhitiz
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does eqn of continuity apply to only incompressible fluids?is there an eqn for compressible fluids?
minger said:In pseudo form, the equation of continuity over a control volume is simply
[tex] \sum m_{in} = \sum m_{out} + \sum m_{accumulated} [/tex]
So, if you have a box with marbles in it, and you put more marbles into it, either you accumulate marbles in the box, or if the box is full, marbles must come out.
For incompressible flow, pressure must remain constant, this means that the number of marbles (think molecules) must remain the same. That means for every marble that comes in, one must go out. However, for compressible flow, there can be an accumulation inside the control volume.
IIRC the actual equation in one of the 4 forms is something like:
[tex] \frac{\partial \rho}{\partial t} + \nabla (\vec{\rho V}) = 0 [/tex]
The second term is called Divergence of Velocity and ends up being a rather important term when deriving the N-S equations.
stewartcs said:For the general case, the RHS should be the time rate change of the mass inside the control volume, not the summation.
[tex] \sum \dot{m}_{in} - \sum \dot{m}_{out} = \Delta \dot{m}_{system} [/tex]
The equation of continuity for incompressible fluids, also known as the continuity equation, is a mathematical expression that describes the relationship between fluid velocity and fluid flow rate. It states that the product of the cross-sectional area of a pipe or channel, fluid velocity, and fluid density is constant throughout the system.
The equation of continuity for compressible fluids is similar to that of incompressible fluids, but it also takes into account changes in fluid density under varying pressure and temperature conditions. This is represented by the addition of a compressibility factor, which is a measure of how much a fluid's density changes with changes in pressure and temperature.
The equation of continuity is used extensively in fluid mechanics, and it has many practical applications. Some examples include calculating the flow rate of water through pipes, designing pumps and turbines for various industries, and predicting weather patterns and ocean currents.
The equation of continuity is derived from the principle of conservation of mass, which states that mass cannot be created or destroyed, only transferred. By applying this principle to a fluid system, we can derive the equation of continuity, which mathematically expresses the conservation of mass in a fluid flow.
The equation of continuity is applicable to both liquids and gases, as long as the fluid is considered to be incompressible or the compressibility factor is accounted for. However, it may not accurately describe the behavior of non-Newtonian fluids, such as non-Newtonian liquids and viscoelastic materials, which have complex flow properties.