Page 119 - Pipelines and Risers

92 Chapter 6

Pipeline Exposed to Accelerated Fluid Flow
A pipeline exposed to an accelerated fluid experiences a force proportional to the
acceleration, this force is called the inertia force. The following expression gives the
transverse inertia force component per unit length of a pipeline:
7T
p
Transverse inertia force, F, = - D C an (6.28)
4
where:
CM = (Ca+1)
Transverse inertia coefficient.
a,, = Transverse water particle acceleration.
p = Density of seawater.
D = Total external diameter of pipe.

The complete Morison’s equation
The formula given above does not take into account that the pipe itself may have a velocity
and acceleration. The inline force per unit length of a pipe is determined using the complete
Morison’s equation.

(6.29)

where:
P sea water density
D outer diameter
U instantaneous (time dependant) flow velocity
Y in line displacement of the pipe
CD drag coefficient
CM inertia coefficient
= (C,+l) where C, is the added mass Coefficient
&& differentiation with respect to time

Drag and Inertia Coefficient Parameter Dependency
In general, the drag and inertia coefficient is given by:
CD = cD(Re,Kc, ,(e/D),(kID),(Az/D)) (6.30)
CM = ‘&(Re,KC,a ,(e/D),(AZ/D)) (6.31)

Reynolds number indicate the present flow regime, @e. laminar or turbulent) and is given as:
UL
Re= - (6.32)
V
where:
U = Now velocity