THE TORQUE ON A ROTATING N-BLADED VANE IN A NEWTONIAN FLUID OR LINEAR ELASTIC MEDIUM

The vane is an n-bladed paddle which rotates with angular velocity-OMEGA in a linear viscoelastic fluid. The blades, of zero thickness, are equally spaced around the axis r = 0, and extend from r = 0 to r = a. The problem is assumed two-dimensional. The stress and fluid velocity (or material displacements) are obtained by a Wiener-Hopf technique for the case of a no-slip boundary condition on the surface of the blades, and for the case of zero shear stress on the blades. The torque M (per unit length) required to rotate the vane in an incompressible newtonian fluid of viscosity-mu may be approximated as M almost-equal-to 4-pi-mu-a2-OMEGA(1 - n-1) to within 1 % for the no-slip boundary condition; with the slip boundary condition the same expression is accurate to within 4 %. Results are also given for the angular dependence and strength of the stress singularity at the tip of each blade.