**4. Forces **

Time histories of the stream wise
load *F*_{x} on the columns
from bores of several different heights were recorded using the load cell.
Figures 4.1 show the time histories for both orientations of the square column
and the circular column, respectively. In most cases the curves have similar
shapes indicating that they could be normalized to collapse into a single
curve. The force record can be normalized with , where *ρ*=
998 kg/m^{3} is the density of
the water during the runs, *h* is the water depth, *b* is the
width of the object perpendicular to the flow and *u* is the flow velocity.
Values of both *h* and *u* are taken from free flow conditions,
i.e. flow without any objects, and the values are time dependent. The normalized
force in this manner is equivalent to the drag coefficient *C _{D}*; here we use the term coefficient of resistance

For the smallest bore, *h*_{1} = 100 mm, the force
on the square column during the impact is about 50 % higher than the force
after the initial impact. For the larger bores, the initial impact becomes less pronounced in comparison to the subsequent 'quasi-steady' drag force. This is because the front face of the bore becomes less steep; hence the mildly sloped front face prevents the impact from "slumming" of the nearly vertical wall of water (Ramsden, 1993; Yeh et al, 2005). Also note that no initial impact force was recorded when the square column was oriented such that the corner faces the flow (Figs. 4.1 b and 4.2 b). The initial impact is less important for the circular column as seen from Figs. 4.1 a and 4.2 a.

a)

b)

c)

Figure 4.1. Temporal variations of the force exerted on a) the square column with one side facing the flow, b) the square column with one corner facing the flow, and c) the circular column.

a)

b)

c)

Figure 4.2. Temporal variations of the nondimensionalized force exerted on a) the square column with one side facing the flow, b) the square column with one corner facing the flow, and c) the circular column.