The power required for doing work in a centrifugal machine (pump or fan) is related to the "q", of the flow (volume) passing through it. The actual formula is P = dp * q where P = Power (watts), dp = change in pressure (d = delta or change, p = pascals, a unit of pressure) and q = volumetric flow in cubic meters per second. Do if you drop either the pressure or the flow, the power required to do the job drops. When you close a damper, you are doing both.
This is related to how VFDs save money by the way. Some people like to claim that VFDs do not save any real energy by pointing ut this fact. You use less energy when you reduce flow in an air duct no matter how you do it, VAV (dampers) or VFD on the motor. But with dampers, you also get turbulence, so that then increases the pressure in the duct (or the fan box if they are inlet dampers), meaning that your dp in that formula goes down. By using a VFD instead, there is a difference in the AMOUNT of total energy savings that you gain by reducing flow, because you no longer create the turbulence that was robbing your duct of efficient air flow.