Page 123 - Aerodynamics for Engineering Students
P. 123
106 Aerodynamics for Engineering Students
Q
Fig. 3.1
Fig. 3.2
via some other path such as €3, there would be some flow components circulating in
the circuit OAPBO. This in turn would imply that the fluid within the circuit
possessed vorticity. The existence of a velocity potential must therefore imply zero
vorticity in the flow, or in other words, a flow without circulation (see Section 2.7.7),
i.e. an irrotational flow. Such flows are also called potential flows.
Sign convention for velocity potential
The tangential flow along a curve is the product of the local velocity component and
the elementary length of the curve. Now, if the velocity component is in the direction
of integration, it is considered a positive increment of the velocity potential.
3.1.2 The equipotential
Consider a point P having a velocity potential 4 (4 is the integral of the flow
component along OP) and let another point PI close to P have the same velocity
potential 4. This then means that the integral of flow along OP1 equals the integral of
flow along OP (Fig. 3.3). But by definition OPPl is another path of integration from
0 to PI. Therefore
4= J qcosPds=
OP
