If you are still unclear why internal flow and airfoil won't create a new rocket engine, think in terms of pressure in a cross-section of the tube where the airfoil is located.
------------------------- ceiling of the tube
low pressure (-p)
------------------------- airfoil
high pressure ( p)
------------------------- floor of the tube
The airfoil has higher pressure below it and lower pressure above it so wants to move up and take the tube with itself. But look at the ceiling and floor of the tube. The floor has higher pressure above it so it experiences a force downwards. The ceiling too experiences a downward force as it has low pressure below it.
Let's calculate these forces:
1. On ceiling: p*A downwards, where A is the horizontal cross-section area of the tube
2. On the floor: p*A downwards
3. On foil: (-p-p)*A downwards = 2p*A upwards
The only area that is to be considered is in the direction of the resultant force which is equal to the horizontal cross-section area of the tube same as the airfoil.
As you can see the upwards and downward forces cancel out and all we have created is internal stress within the tube's structure. Always remember the concept of internal and external forces on a system.
