Offshore Structure Loads and Strength - Offshore Structures: Design, Construction and Maintenance - page 53

were not developed until 1950, when the Morison equation was presented and the
wave forces on a vertical pipe were shown to be as illustrated in Figure 2.8 :

F = F D + F I (2.15)

where F D is the drag force and F I is the inertia force.
● Drag force: The drag force due to a wave acting on an object can be found by:

CdV 2 A

F D =

= ρ

1 2 (2.16)

where F D is the drag force (N), Cd is the drag coefficient (no units), V is the
velocity of the object (m/s), A is the projected area (m 2 )and ρ is the density of

water (kg/m 3 ).

Inertia force: The inertia force due to a wave acting on an object can be found by: ●

F I = πρ aCmD 2

= 4 (2.17)

where F I is the inertia force (N), Cm is the mass coefficient (no units), a is the
horizontal water particle acceleration (m 2 /s), D is the diameter of the cylinder
(m) and is the density of water (kg/m 3 ).

ρ

Wave Load Calculation

The values of Cd and Cm are dimensionless and the values most often used in
the Morison equation are 0.7 and 2.0, respectively. API recommends 0.65 and
1.6, respectively, for smooth surfaces or 1.05 and 1.2, respectively, for rough
surfaces, such as surfaces with marine organism growth.

●

Wave
propagation

Vertical
cylinder

Force
distribution

Crest
elevation

Wave
height

Air

MSL

Water

Sea bed

FIGURE 2.8 Wave force distribution on a vertical pipe.