Civil Engineering Reference
In-Depth Information
C
p
=
f
(π
1
, π
2
, π
3
,…)
(4.6)
Examples of relevant non-dimensional groups are:
•
h/z
0
(Jensen number; where
z
0
is the roughness length as discussed in Section 3.2.1);
•
I
u
, I
υ
, I
w
the turbulence intensities in the approaching flow;
•
(ℓ
u
/h), (ℓ
v
/h), (ℓ
w
/h)
representing ratios of turbulence length scales in the approaching
flow to the characteristic body dimension; and
•
(Uh/υ),
Reynolds number, where
υ
is the kinematic viscosity of air.
Equation (4.6) is relevant to the practice of wind-tunnel model testing, in which
geometrically scaled models are used to obtain pressure (or force) coefficients for
application to full-scale prototype structures (see Section 7.4). The aim should be to
ensure that all relevant non-dimensional numbers (π
1
, π
2
, π
3
, etc.) should be equal in both
model and full scale. This is difficult to achieve for all the relevant numbers, and methods
have been devised for minimizing the errors resulting from this. Wind-tunnel testing
techniques are discussed in Chapter 7.
4.2.4
Reynolds number
Reynolds number
is the ratio of fluid inertia forces in the flow to viscous forces and is an
important parameter in all branches of fluid mechanics. In bluff-body flows, viscous
forces are only important in the surface boundary layers and free shear layers (Section
4.1). The dependence of pressure coefficients on Reynolds number is often overlooked
for sharpedged bluff bodies such as most buildings and industrial structures. For these
bodies, separation of flow occurs at sharp edges and corners such as wall-roof junctions,
over a very wide range of Reynolds number. However, for bodies with curved surfaces
such as circular cylinders or arched roofs, the separation points
are
dependent on
Reynolds number, and this parameter should be considered. However, the addition of
turbulence to the flow reduces the Reynolds number dependence for bodies with curved
surfaces.
4.3
Flat plates and walls
4.3.1
Flat plates and walls normal to the flow
The flat plate, with its plane normal to the air stream, represents a common situation for
wind loads on structures. Examples are elevated hoardings and signboards, which are
mounted so that their plane is vertical. Solar panels are another example but, in this case,
the plane is normally inclined to the vertical to maximize the collection of solar radiation.
Free-standing walls are another example, but the fact that they are attached to the ground
has a considerable effect on the flow and the resulting wind loading. In this section, some
fundamental aspects of flow and drag forces on flat plates and walls are discussed.
