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If we have a steady isothermal incompressible flow (with non-zero velocity field), the density must be constant and uniform, right?

Can we conclude that the number of fluid elements(fluid parcels/very tiny fluid particles, from which the flow is made of) in the(per) unit volume is the same? To rephrase it, is the number of fluid particles in the area where the flow is very slow and the area with higher velocity (per unit volume) same?

The problem here is that if we replace the flow with infinite number of discrete fluid parcels, we can clearly see that the number of parcels does not remain uniform if we have the velocity gradient. But if we assume that the number of parcels are not uniform, how can we say that the density is constant and uniform?

If we have a steady isothermal incompressible flow (with non-zero velocity field), the density must be constant and uniform, right? so:

Can we conclude that the number of fluid elements(fluid parcels/very tiny fluid particles, from which the flow is made of) in the(per) unit volume is the same? To rephrase it, is the number of fluid particles in the area where the flow is very slow and the area with higher velocity (per unit volume) same?

The problem here is that if we replace the flow with infinite number of discrete fluid parcels, we can clearly see that the number of parcels does not remain uniform if we have the velocity gradient. But if we assume that the number of parcels are not uniform, how can we say that the density is constant and uniform?

If we have a steady isothermal incompressible flow (with non-zero velocity field), the density must be constant and uniform, right?

If yes, can we conclude that the number of fluid elements(fluid parcels/very tiny fluid particles, from which the flow is made of) in the(per) unit volume is the same? To rephrase it, is the number of fluid particles in the area where the flow is very slow and the area with higher velocity (per unit volume) same?

If we have a steady isothermal incompressible flow (with non-zero velocity field), the density must be constant and uniform, right?

Can we conclude that the number of fluid elements(fluid parcels/very tiny fluid particles, from which the flow is made of) in the(per) unit volume is the same? To rephrase it, is the number of fluid particles in the area where the flow is very slow and the area with higher velocity (per unit volume) same?

The problem here is that if we replace the flow with infinite number of discrete fluid parcels, we can clearly see that the number of parcels does not remain uniform if we have the velocity gradient. But if we assume that the number of parcels are not uniform, how can we say that the density is constant and uniform?

If we have a steady isothermal incompressible flow (with non-zero velocity field), the density must be constant and uniform, right?

If yes, can we conclude that the number of fluid elements(very tiny fluid particles, from which the flow is made of) in the(per) unit volume is the same? To rephrase it, is the number of fluid particles in the area where the flow is very slow and the area with higher velocity (per unit volume) same?

If we have a steady isothermal incompressible flow (with non-zero velocity field), the density must be constant and uniform, right?

If yes, can we conclude that the number of fluid elements(fluid parcels/very tiny fluid particles, from which the flow is made of) in the(per) unit volume is the same? To rephrase it, is the number of fluid particles in the area where the flow is very slow and the area with higher velocity (per unit volume) same?