By saying that the velocity of the flow would increase, you have made the assumption that there is a force (the pump behind you tap) forcing the flow rate to be (approximately) constant.
This is not the case here, just having a tub of water with a hole on the bottom in just maintaining the...
It is taught that the classical treatment of the diatomic atom would give a heat capacity of $7/2$ due to 7 degrees of freedom, (three translational momentum, two rotational momentum, on vibration momentum and on vibration position).
This is based on the Hamiltonian looking like:
$$
H =...