A New Mechanical Analogy for the Flow of Compressible Fluid

between upstream and downstream conditions and are symmetrically placed. The nature of the relationship between complex hodograph parameter and complex velocity potential shows that similar velocity variations will occur at similar points in the complex velocity potential field when the latter has been determined in the physical plane. As the Mach Number is increased, the upstream and downstream flow angles, the stagger, and the stream deflection all decrease. The camber angle of the airfoils, given by the diameter of the hodograph circle, also decreases. The cascade solidity will decrease at the same time, since the potential gradient at any point in the physical plane is greater than the streamfunction gradient and since the ratio between the two increases with increasing Mach Number. The comparison between cascades at different Mach Numbers described here is for airfoils with cusp ends. Comparison for airfoils with rounded leading edges is possible only if the edge effect is neglected, since the relationships among angles really imply that the included angle of the leading edge will decrease along with the other flow angles in the field. The relations obtained here appear to imply those obtained by Woolard using the Prandtl-Glauert approach when the limiting case of small stream deflections is considered.