In fluid mechanics and in case of Hydraulic turbines, we use the velocity triangles to solve problems. But I don't understand what does whirl velocity means in those triangles... I tried to search the internet, but I got no satisfactory answer there..

Just had a quick search for whirl velocity and I understand it as the velocity radially around the turbine, i.e. the velocity of the fluid in the plane of the turbine blade rotation, and thus using the triangle and Pythagoras. Linear velocity squared (V^2), Work velocity squared (Vw^2), Absolute velocity squared (Va^2), Sqrt((V^2) x (Vw^2)) = Va So the whirl velocity is combined with the linear velocity to get the absolute velocity the fluid. I hope this helps