The angular velocity, rotation, vorticity, and circulation in fluid mechanics are specific terms which are somehow related to each other. Although these terms are not so straight to apply, they are well demonstrated in many textbooks. Is the flow circulation around the desired airfoil linked to the expected airfoil lift?
Different important terms, angular velocity, rotation, vorticity, and circulation, are studied in fluid mechanics courses. Mathematically, vorticity is defined as the curl of the flow velocity field. Hence, the vorticity is a vector field that gives a microscopic measure of the rotation at any point in the fluid. The flow circulation about a closed contour, say around an airfoil, in a fluid is defined as the line integral that is evaluated along the contour of the component of the velocity vector that is locally tangent to the contour. Thus, the circulation is a scalar integral quantity, which is a macroscopic measure of flow rotation for a finite area of the fluid. The circulation can be described as the amount of force that pushes along the closed boundary or path. Hence, the circulation can be considered as the total “push” one gets when going along the contour. Here, for a symmetrical airfoil with zero angle of attack there would be zero circulation leading to zero resultant force or zero lift. Therefore, a circulation should be generated by playing in the geometrical or operational conditions in order to have lift.
The vorticity and the angular velocity is Somewhat same as both describe the angular change of a fluid particle with respect to a point. However vorticity is essentially a fluid related term whereas the angular velocity term can be used for any short of motion.
For comparison you can assume movement as vorticity and speed as the angular velocity .
Rotation on other hand is the spinning of the fluid particle.
for example earth moves around sun is similar to vorticity and have a angular velocity of 2pi radian per year and the spinning of earth can be taken as rotation with angular velocity of 2pi redian per day.
Now circulation and vortex is again similar but the difference is that if the movement of the particle is essentially in same plane then it can be termed as circulation and if the particle changes its plane but rotates about an axis the it is a vortex.every circulation forms a vortex.
All the things i have mentioned above are in scale refernece however things changes in vector and tensor form.
the lift is entirely different thing here.
suppose you are facing a flow of any fluid .....say air .....if you feel pushed then it is a drag and if you feel to rise up or down then it is lift.
simply the force you experience in the direction of flow is drag and force you experience perpendicular the direction of flow is lift.
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