Modelica.Fluid.Vessels.ClosedVolume roots

[HansOlsson]

The model Modelica.Fluid.Vessels.ClosedVolume contains:

    vesselArea = pi*(3/4*V)^(2/3),
    heatTransfer(surfaceAreas={4*pi*(3/4*V/pi)^(2/3)}));

There is a proposal to introduce the nth root in Modelica that can be used instead of x^(2/3) (and help unit-checking), since Modelica does not have rational numbers, and that could be used directly for heatTransfer.surfaceAreas, which just computes radius from Volume and then Area based on that. As documented a Sphere has: Volume 4*pi*r^3/3 and Area 4*pi*r^2, so it all makes sense.

But I don't understand the corresponding formula for vesselArea.

[HansOlsson]

If it were vesselArea = pi*(3/4*V/pi)^(2/3) I would understand it.

That is the cross-section area of the spherical volume - and it doesn't seem to make sense to have a port larger than that, right? However, that leaves a factor (pi)^(2/3) without explanation.