The horsepower is directly related to pressure and flow.
HP = Q * H * SG / (3960 * EFF)
Where:
P = Power, hp
Q = Flow Rate, gpm
S = Specific Gravity of fluid
H = Head height, ft
EFF = Efficiency coefficient
Since Q = AV; Yes the pump casing size is somewhat related to the pump HP. But since the pump can be low to high speed and the volume is inversely proportional to the speed, there is no rule of thumb.