Subscript AB denotes diffusivity of species A diffusing into species B. Under the assumption that formula_101, these equations become equivalent to the momentum balance. Thus, for Prandtl number formula_102 and Schmidt number formula_103 the Blasius solution applies directly. Accordingly, this derivation uses a related form of the boundary conditions, replacing formula_104 with formula_105 or formula_106 (absolute temperature or concentration of species A). The subscript S denotes a surface condition. Using the streamline function Blasius obtained the following solution for the shear stress at the surface of the plate. And via the boundary conditions, it is known that  We are given the following relations for heat/mass flux out of the surface of the plate  So for formula_116  where formula_118 are the regions of flow where formula_105 and formula_106 are less than 99% of their far field values. Because the Prandtl number of a particular fluid is not often unity, German engineer E. Polhausen who worked with Ludwig Prandtl attempted to empirically extend these equations to apply for formula_121. His results can be applied to formula_122 as well. He found that for Prandtl number greater than 0.6, the thermal boundary layer thickness was approximately given by:  From this solution, it is possible to characterize the convective heat/mass transfer constants based on the region of boundary layer flow. Fourier's law of conduction and Newton's Law of Cooling are combined with the flux term derived above and the boundary layer thickness. This gives the local convective constant formula_127 at one point on the semi-infinite plane. Integrating over the length of the plate gives an average  Following the derivation with mass transfer terms (formula_98 = convective mass transfer constant, formula_97 = diffusivity of species A into species B, formula_131 ), the following solutions are obtained:  These solutions apply for laminar flow with a Prandtl/Schmidt number greater than 0.6. Many of the principles that apply to aircraft also apply to ships, submarines, and offshore platforms. For ships, unlike aircraft, one deals with incompressible flows, where change in water density is negligible (a pressure rise close to 1000kPa leads to a change of only 2–3 kg/m3). This field of fluid dynamics is called hydrodynamics. A ship engineer designs for hydrodynamics first, and for strength only later.