Theory of radial equilibrium
Consider a small element of fluid of mass dm, shown in Figure 6.2, of unit depth and subtending an angle dθ at the axis, rotating about the axis with tangential velocity, cθ, at radius r. The element is in radial equilibrium so that the pressure forces balance the centrifugal forces:
Equation (6.8) clearly reduces to Eq. (6.6b) in a turbomachine in which equal work is delivered at all radii and the total pressure losses across a row are uniform with radius.
Equation (6.6b) may be applied to two sorts of problem: the design (or indirect) problem, in which the tangential velocity distribution is specified and the axial velocity variation is found, or the direct problem, in which the swirl angle distribution is specified, the axial and tangential velocities being determined.