What is Pumps and fans?
Machines that raise the pressure of a fluid. The pressure rise, the flow and the efficiency set the power they need.
To push a fluid through pipes and equipment you need to know how much pressure rise it takes and how much power that needs.
Lifting water into a tank higher up takes a pump whose head matches the height.
A pump (liquid) is given by its head, its outlet pressure or a head curve; a fan (gas) by its pressure rise or a pressure curve. Curves are for the rated speed and are converted to another speed with the affinity laws. All shaft power is taken to go into the fluid, which gives the outlet temperature. Fans are modeled as incompressible up to a pressure ratio of 1.07 and refused beyond.
The pump's pressure rise is \Delta p = \rho g H and its shaft power
W = \dot{V}\,\Delta p / \eta
with the outlet at h_{\mathrm{out}} = h_{\mathrm{in}} + W/\dot{m}. Affinity laws: the flow scales with the speed and the head (pressure) with its square (H(Q, n) = (n/n_0)^2 H_0(Q\,n_0/n)).
Curves are not extrapolated. NPSH (cavitation) is not evaluated yet.