A practical one-parameter polynomial type integral method is developed in this paper for laminar incompressible plane and thin axisymmetric boundary layer flow with transpiration and pressure gradient. The method features the use of approximations for the velocity distribution that are based on second and third order polynomial approximations for the distribution in shear stress. These approximations are used to develop solutions to the integral momentum equation for similar and nonsimilar flows. The accuracy of the method is generally within about 3 percent, except near separation where the error can reach 10 to 15 percent. The range of conditions for which the method applies covers a fairly wide range of blowing and suction rates and pressure gradients which encompasses plane and axisymmetric stagnation flows and extends to separation. Because of its fundamental nature, the approach provides a basis for generalization to heat and mass transfer and turbulent flow, and provides a framework for the development of more accurate multiple parameter integral methods for transpired boundary layer flow.

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