The flow rate through a cross-section, A, of the circumferential angle, φ, is generally calculated as:
Using Qφ=φ / (2π) Qi+Q0 results in an equation to calculate the circumferential angle, φ, dependent on the outer radius ra:
b(r) is a geometrical function which is defined according to the shape of the cross-section. The velocity cu is chosen in accordance with the design instructions. Under Design rule, two alternatives can be selected.
For all velocity-based rules the area for each cross section is calculated using a linearly increasing volume flow Qφ starting at Q0 for φ=0 (blind volume flow) and an assumed velocity distribution c over r. While Qφ depends on a total reference volume flow Qi, the velocity distribution is defined by a reference cu at r4 and one of the following velocity rules. Note that both reference values can be chosen manually by deactivating Flow properties from inlet.
Experience has shown that the losses can be greatly minimized if the volute housing is dimensioned such that the fluid flows in accordance with the principal of conservation of angular momentum. The cross-section areas are therefore designed in accordance with the principal of conservation of angular momentum, i.e. angular momentum exiting the impeller is constant. In addition, an exponent of angular momentum, x, can be chosen so that the principle curx = const. is obeyed. When x=1, the angular momentum is constant. For the extreme of x=0, the circular component of the absolute velocity cu remains constant at the impeller outlet.
The integral can be explicitly solved for simple cross-section shapes (rectangles, trapezoids, circles). For other, arbitrary, shapes, it can be solved numerically.
Alternatively, it can be beneficial to design the volute with a constant velocity in all cross-sections of the circumference. According to Stepanoff, this constant velocity can be determined empirically: . The constant ks can be determined dependent on the specific speed nq (see Approximation function).
Note, for manually defined reference velocities cu,4, ks has no influence because c is constant over r.
Contrary to velocity-based rules the geometry progression is defined directly. The end cross section is defined by radius or cross section area, the distribution by Radius-, Area- or Area/Radius-progression (Set Progression).