Hi all. I am revisiting things about potential flows. So, I believe the assumptions of potential flows shall be the irrotationality and the ignorance of viscosity. And I am studying the flow past a cylinder with and without circulation. Without circulation, there is no lift force but when there is circulation, then there is lift force. The lift force is due to the inclusion of circulation, which shall be equivlent to the inclusion of vorticity, right? For cylinder with circulation, the vorticity is concentration in the center of the FREE vortex introduced, right? Would this sort of contradicts the assumption of irrotational flow? And it seems to me that this example (cylinder with circulation) is applied to study real flows in daily life, right? Since life force is always observed e.g in airfoils and spinning of gold ball (sudden fall) etc. So there shall be some relationship between the real life examples and this cylinder with circulation, isn't it? For the case of airfoil, while the cylinder with circulation study ignores viscosity, but the circulation needed for the airfoil to generate a lift force is actually caused by the viscosity in the boudary layer, am I correct? So, I understand this as follows: Yes, the potential flows ingores the viscosity but it still generate lift force because vorticity is added deliberately. (Somehow vorticity is added) But in real life, this vorticity is caused by the viscous effect in the boundary layer, which genrates some vortex and hence vorticity is introduced. Am I thinking correctly? And for the case of spinning ball, it is the viscoity in the boundary layer that drags the air around the ball and hence vorticity is diffused. And the study of potential flows on cylinder with circulation can be applied to qualitative explain the life force because there is some circulation which is deliberately added around the cylinder by adding a free vortex, right? So, if the fluids in the world is really of zero viscosity, then the spinning ball and rotating cylinder and airfoil cannot produce lift, right? Since there is actully no circulation and source of circulation, what do you think?