Hydraulic Structures: Fourth Edition

WORKED EXAMPLES 621

Solution

The external diameter of the pipe is 275 32  200 507 mm. The weight
of concrete is 1/4π(0.507^2 0.307^2 ) 2700 9.813.39 103 Nm^1. The
weight of steel is 1/4π(0.307^2 0.275^2 ) 7800 9.811.13 103 Nm^1. The
weight of the pipe in air is 4.52 103 Nm^1. The buoyancy is 1/4π
0.507^2  1030 9.812.04 103 Nm^1. The submerged weight of the pipe
is (4.52 2.04) 103 2.48 103 Nm^1.
From Fig. 14.4, for d20 m, T9 s and L105 m,

H6 m, k 2 π/1050.06 m^1 ,  2 π/90.7 s^1.

From equation (14.16)

u

6

2

 sint

1.4 sint.

MORISON EQUATION (14.69)

In determining the wave force, the component of velocity normal to the
pipeline is considered. The algebraic sum of the velocity of the current and
the particle velocity due to the wave is

u(0.5 1.4 sint) cos 60°.

DRAG TERM

CD

2

|u|uD1.1 | 0.5^ 1.4 sint| (0.5^ 1.4 sint)

0.507cos^2 60°

71.8 | 0.5 1.4 sint| (0.5 1.4 sint)(N m^1 ).

INERTIA TERM



6

2



2

cosh costcos 60°

costcos 60°(m s^2 ).

The inertia force is

3.1 1030 

π

4

0.507^2 cos 60° cost322.3 cost(N m^1 ).

[0.06( 19.74620)]



sinh(0.0620)

2 π



9

∂u



∂t

1030



2

cosh[0.06( 19.74620)]



sinh(0.0620)

2 π



9