Euler may have been talking about an actual tube in which the flow of fluid took place. Faraday thought that the lines of force had a physical existence. Maxwell thought in terms of an imaginary tube in which a flow existed. What is the actual situation? Are flux tubes are real or imaginary?
We know that an actual barrier has physical properties associated with it. These are the boundary conditions. But what is the situation where no physical boundary exists? There are no boundary conditions acting. But a flow may define a boundary expecially if a "steady" flow exists that doesn't change with time. The sides of the flux tube are defined by the fact that the net flow across the boundary is zero. So in a sense a flux tube exists. It is the boundary that is imaginary.
The component of the forces acting on the fluid normal to an imaginary boundary would have to be zero or there would be an acceleration of the fluid across the boundary. Within a liquid or gas there may be shear forces present but it makes no difference if they are parallel to the surface. The physical barrier of an actual tube wall can also introduce a pressure which counters any forces acting on the fluid. But an imaginary tube has no constraints associated with it.
This is the situation for hydrodynamics dealing with a real fluid. For Electromagnetism and Optics the situation is somewhat less certain. One cannot measure the properties of a hypothetical aether and that makes any aether theory occult. But the dilemma that remains if there is no aether is how do we explain action at a distance for electromagnetic forces? The only rational conclusion is that there is a field present whose nature is unknown. Our knowledge of the nature of the force field is deficient. We can't define a density or velocity of flow for the aether. All that we can observe is an effect on test charges.
For Optics the situation was the same for the flux of light at the time that Photometria was written. Only relative measurements could be made. Today the situation is different and we can define a flux of energy. We can measure the rate at which energy flows across a given surface in a given time. A measurable flux exists for Quantum Optics.
What makes modern Electromagnetism difficult to understand is that a discussion of the aether is suppressed. We have no direct evidence for the existence of an aether. But what we call a "vacuum" may not be a void. It still has physical properties since there are fields present. In Relativity there is frame dragging. In Quantum Mechanics the lowest energy state is not zero energy. In Quantum Optics there is a vacuum state. So the question of the existence of an aether may still be an open one. One can doubt that an aether does not exist. Has the case for its nonexistence been proven?