Page 185 - Aerodynamics for Engineering Students

168 Aerodynamics for Engineering Students

Fig. 4.7

The vertical static pressure force or buoyancy h, on the circular boundary is the sum
of the vertical pressure components acting on elements of the periphery. At the
element subtending SO at the centre of the aerofoil the static pressure is p and the
local velocity is the resultant of V and the velocity v induced by the circulation.
By Bernoulli's equation
1
1
PO + - PV' = p + -p[v2 + VZ + ~VV e]
2
sin
2
giving
p =po - pVvsin8
if v2 may be neglected compared with V2, which is permissible since r is large.
The vertical component of pressure force on this element is
-pr sin 8 St)

and, on substituting for p and integrating, the contribution to lift due to the force
acting on the boundary is
2iT
lb = -l (PO - pVvsine)rsin ode
(4.7)
= +pVvrr
with po and r constant.