The non-symmetrical flow generated by flat and cambered laminae at angles of attack is at first modelled by vorticity distributions via classical linearized theory. Here, in contrast to the analysis of symmetrical sections, we encounter integral equations in the determination of the vorticity density because the local transverse component of flow at any one point depends upon the integrated or accumulated contributions of all other elements of the distribution. Pressure distributions at non-ideal incidence yield a square-root-type infinity at the leading edge because of the approximations of first order theory. Lighthill's (1951) leading edge correction is applied to give realistic pressure minima at non-ideal angles of incidence.

Our interest in pressure minima of sections is due to our concern for cavitation which can occur when the total or absolute pressure is reduced to the vapor pressure of the liquid at the ambient temperature. Since cavitation may cause erosion and noise it should be avoided or at least mitigated which may possibly be done by keeping the minimum pressure above the vapor pressure. This corresponds to maintaining the (negative) minimum-pressure coefficient Cpmin higher than the negative of the cavitation index.

At this point we shall not go deeper into the details of cavitation which is postponed until Chapter 8. Instead we shall continue our theoretical development with flat and cambered sections.

THE FLAT PLATE

We now seek the pressure distributions and the lift on sections having zero thickness but being cambered and, in general, set at any arbitrary (but small) angle of attack to the free stream, U. Consider a flat plate at small angle α.