A linear equation is mathematically derived for hydrodynamic forces on a marine riser under effects of free surface and floating-vessel motion using a velocity-potential method. It accounts for inertia and wave damping forces, including the force caused by riser motion, and empirically includes the drag force caused by viscosity. The equation, when reduced to a simpler form, is basically identical to the semi-empirical Morison equation for the inertia and drag forces. Theoretical validity of the simpler equation and the Morison equation is discussed. Previously, practical, semi-empirical force equations on the riser have been suggested, ignoring the effects of the free surface and the wave damping. The equations in current practice are compared with the present simpler equation.

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