Morison equation

[1] The Morison equation is used to estimate the wave loads in the design of oil platforms and other offshore structures.

The inertia force is of the functional form as found in potential flow theory, while the drag force has the form as found for a body placed in a steady flow.

In the heuristic approach of Morison, O'Brien, Johnson and Schaaf these two force components, inertia and drag, are simply added to describe the inline force in an oscillatory flow.

The transverse force—perpendicular to the flow direction, due to vortex shedding—has to be addressed separately.

The Morison equation contains two empirical hydrodynamic coefficients—an inertia coefficient and a drag coefficient—which are determined from experimental data.

[4][5] The descriptions given below of the Morison equation are for uni-directional onflow conditions as well as body motion.

, the Morison equation gives the inline force parallel to the flow direction:[6] where For instance for a circular cylinder of diameter D in oscillatory flow, the reference area per unit cylinder length is

, the Morison equation becomes:[6] where the total force contributions are: Note that the added mass coefficient

Flow forces according to the Morison equation for a body placed in a harmonic flow, as a function of time. Blue line: drag force; red line: inertia force; black line: total force according to the Morison equation. Note that the inertia force is in front of the phase of the drag force: the flow velocity is a sine wave , while the local acceleration is a cosine wave as a function of time.
Wave loading on the steel jacket structure of a Production Utilities Quarters Compression (PUQC) platform in the Rong Doi oil field, offshore Vietnam (see Oil megaprojects (2010) ).