From the principle of conservation of mass flow follows the continuity equation q_m = q_V \cdot A \cdot v \cdot \rho = \mathrm{const.}
For a flow condition in which no density changes occur, the volume flow q_V is also constant. Thus, for example, for a pipe with a widening cross-section, the result is as shown in Figure 2.4:
A_{\mathrm{I}}\cdot v_{\mathrm{I}} = A_{\mathrm{II}}\cdot v_{\mathrm{II}} = A_{\mathrm{III}}\cdot v_{\mathrm{III}}
Figure 2.4.: Pipe with widening cross section
This also applies to a fan, provided that the compression or expansion of the pumped medium can be neglected (cf. DIN EN ISO 5801).