EM 1110-2-1100 (Part II)
30 Apr 02
EXAMPLE PROBLEM II-7-6
FIND:
The vessel sinkage and return flow velocity between the vessel hull and the channel bottom and
sides.
GIVEN:
A C9 containership has a length of 262 m, a beam of 32 m, and a fully loaded draft of 12 m. The C9
containership with a midsection wetted cross section area of 384 m2 is moving at a speed of 6 knots (3.09 m/s) in
a channel 137 m wide and 15 m deep. This is a typical scenario for deep-draft vessels entering a harbor through
a one-way entrance channel.
SOLUTION:
The vessel Froude number is
3.09
' 0.26
F'
9.81 (15)
and the blockage ratio is
384
S'
' 0.19
137 (15)
From Figure II-7-43 at the intersection of F = 0.26 and S = 0.19, the dimensionless drawdown is approximately
D = 0.02. The vessel sinkage is then given by
∆d ' 15 (0.02) ' 0.30 m
The return velocity is calculated from Equation II-7-25 as
137 (15)
&1
' 0.81 m/s
Vr ' 3.09
137 (15 & 0.3) & 384
Thus, channel depths must include additional clearance to accommodate the vessel drawdown and a substantial
return velocity flow can lead to scour along the channel banks.
(h) As a vessel travels in a channel, continuity of flow causes a return flow velocity to develop between
the vessel hull and the channel bottom and sides. This return flow velocity Vr can be calculated for a
rectangular channel and vessel cross section (as depicted in Figure II-7-42) from
bd
Vr ' Vs
&1
(II-7-25)
b (d & ∆ d) & Am
(i) Particularly for vessel/channel conditions that produce a large blockage ratio (S) and for high vessel
speeds, a substantial return flow velocity can develop. Channel bottom scour and damage to reveted channel
sides may result.
(5) Ship maneuverability in restricted waterways.
(a) The pressure distribution along the hull of a vessel will also cause lateral forces and horizontal
moments to act on the vessel when it passes another vessel or moves in close proximity to a channel bank or
other large structure. These effects affect all sizes of ships, but are particularly dangerous for larger vessels.
Figure II-7-44 shows a pressure field for moving vessels, where the plus and minus signs indicate the relative
pressures along the side of the hull.
II-7-62
Harbor Hydrodynamics
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