. Components of  in Rectangular and Cylindrical Coordinates The rate of deformation is important in characterizing flows. As described earlier, material properties like viscosity can depend on the rate of deformation. Various forms for simple deformation in basic orthogonal coordinate systems can be used to solve many interesting problems. For Newtonian fluids, we have ij =  ij . Rectangular Coordinates(x, y, z--right hand rule with x rotating into y to give z) xx . = 2 vx x vx + vy y x xy . yx = yy . vx + vz z x xz . zx = vy y = 2 zz . vy + vz z y yz . zy = vz z = 2 Extensional flow components Shear flow components

. . . . . . . . (1 v + vr) (1 vz + v) ( vz + vr) Cylindrical Coordinates(r, , z) rr . = 2 vr r r . r .  ( v ) + 1 vr) r r r  = = ( r  . = 2 (1 v + vr) r  r z . = (1 vz + v) r  z z = zz . = 2 vz z zr . rz = . ( vz + vr) r z =