This article is from the Boats FAQ, by John F. Hughes with numerous contributions by others.
The answer, verbatim from mp, is:
The formula yacht designers use is called Crouch's formula.
It takes into account the weight and horsepower at the
propeller, and assumes a 50"% to 60"% efficient prop.
Most props fall into this range. Note that it doesn't take
into account the boat length, as that doesn't matter with
V = C/((DISP/HP)**.5)
Where V = boat speed in knots (1 knot=1.15 mph)
C = Constant (depends on boat type)
DISP = Displacement (pounds)
Note that boat manufacturers usually give
innacurate numbers for displacement,
typically on the low side
HP = Horsepower available at the propeller
For comparison sake, here are some average values of C:
150 Typical lightweight, planing cruiser 180 High Speed Runabout 200-230 Race boats, hydroplanes etc.