SLOW VISCOUS-FLOW DUE TO THE ROTATION OF 2 FINITE HINGED PLATES

Two-dimensional slow viscous flow due to the rotation of two finite hinged plates in an unbounded medium is investigated on the basis of the Stokes approximation under the condition that the fluid velocity remains finite everywhere. The symmetric flow caused when the plates rotate oppositely about the vertex and antisymmetric flow due to rotation of the plates as a whole are considered separately. A formal expression for the flow is obtained by solving a pair of simultaneous Wiener-Hopf equations. The velocity induced at infinity is given as a function of the angle between the plates and the asymptotic behavior of the flow near the vertex are discussed. Normal and shear forces and moment exerted on each plate are also calculated.