Profile drag (or boundary-layer drag)

The profile drag is the sum of the skin-friction and form drags. See also the formal definition given at the beginning of the previous item.

Comparison of drags for various types of body

Normal flat plate (Fig. 1.14)

In the case of a flat plate set broadside to a uniform flow, the drag is entirely form drag, coming mostly from the large negative pressure coefficients over the rear face. Although viscous tractions exist, they act along the surface of the plate, and therefore have no rearwards component to produce skin-friction drag.

Fig. 1.14 Pressure on a normal flat plate

Parallel flat plate (Fig. 1.15)

In this case, the drag is entirely skin-friction drag. Whatever the distribution of pressure may be, it can have no rearward component, and therefore the form drag must be zero.

Circular cylinder (Fig. 1.16)

Figure 1.16 is a sketch of the distribution of pressure round a circular cylinder in inviscid flow (solid lines) (see Section 3.3.9 below) and in a viscous fluid (dotted lines). The perfect symmetry in the inviscid case shows that there is no resultant force on the cylinder. The drastic modification of the pressure distribution due to viscosity is apparent, the result being a large form drag. In this case, only some 5% of the drag is skin-friction drag, the remaining 95% being form drag, although these proportions depend on the Reynolds number.

Aerofoil or streamlined strut

The pressure distributions for this case are given in Fig. 1.13. The effect of viscosity on the pressure distribution is much less than for the circular cylinder, and the form drag is much lower as a result. The percentage of the total drag represented by skin – friction drag depends on the Reynolds number, the thickness/chord ratio, and a number of other factors, but between 40% and 80% is fairly typical.

Fig. 1.15 Viscous tractions on a tangential flat plate

Fig. 1.16 Pressure on a circular cylinder with its axis normal to the stream (see also Fig. 3.23)

Rg. 1.17 The behaviour of smoke filaments in the flows past various bodies, showing the wakes, (a) Normal flat plate. In this case the wake oscillates up and down at several cycles per second. Half a cycle later the picture would be reversed, with the upper filaments curving back as do the lower filaments in this sketch, (b) Flat plate at fairly high incidence, (c) Circular cylinder at low Re. For pattern at higher Re, see Fig. 7.14. (d) Aerofoil section at moderate incidence and low Re

The wake

Behind any body moving in air is a wake, just as there is a wake behind a ship. Although the wake in air is not normally visible it may be felt, as when, for example, a bus passes by. The total drag of a body appears as a loss of momentum and increase of energy in this wake. The loss of momentum appears as a reduction of average flow speed, while the increase of energy is seen as violent eddying (or vorticity) in the wake. The size and intensity of the wake is therefore an indication of the profile drag of the body. Figure 1.17 gives an indication of the comparative widths of the wakes behind a few bodies.