Purpose of this sheet
This sheet can be used to calculate the distributed drag force on a submerged horizontal pipe/cable subjected
to waves represented by Stoke’s nth order wave theory (deep water conditions)
What is ‘drag’ force?
The laid and suspended pipelines are subjected to various external forces. One of the primary external forces is drag force which is caused by the relative flow direction of wave and current together. The direction of the force can be
split into vertical and horizontal components: each is affected by the flow rate in the same direction.
Drag force is a function of exposed cross-section and relative flow rate. The proportionality to the relative flow rate is with the power of 2. The drag force, as defined by Morison, is given by the following formulation:
Where Cd is the coefficient relating drag force to the variables mentioned above.
As per DNV-RP-C205 recommended practice on Environmental conditions and environmental loads, the drag
coefficient is a function of Reynnold’s number which is a non-dimensional parameter correlating flow rate vs the
pipe dimension. The drag coefficient is also a function of the roughness of the surface of the pipeline.
Note that in a subcritical flow (Re <10^6) a rough pipe does not necessarily lead to a high drag coefficient.
Thirdly the velocity is decided on the position of the pipeline with respect to the free-surface. The flow velocity has a hyperbolic relationship with the water depth, while the current is correlated with a power function.
A combination of wave and current is employed for calculating combined fluid flow velocity.
Please explore the sheet in Calcsheet!
How does the sheet calculate?
This sheet simply takes pipe dimensions, positions, and incoming wave and current directions for calculation.
At the bottom of the sheet, drag force is calculated.
This sheet is not useful for shallow water assessment (Ursell number >30) Only deep water
cases with Ursell number <30 are with the scope of this sheet.
To aid the user, the applicability of the sheet is indicated in the calculation sheet
The sheet is not applicable for vertical pipes.
Hydrodynamics of offshore structures, S.K. Chakrabarti
Offshore Hydromechanics, JMJ Journee WW Massie