The dynamics of high speed streams of solar plasma emanating from a coronal hole is investigated by use of a two-fluid model with polytropic equations of state. Steady outflow is considered along a flow tube which has a radial orientation with respect to the Sun, and a cross-sectional area proportional to r' where r is the heliocentric radius and s is a divergence parameter (~2). All the flow variables are assumed to be functions of r only. The equations of continuity, momentum and state may be used to obtain a single, nonlinear, ordinary differential equation for the outflow velocity, and the problem reduces to the numerical solution of three pairs of simultaneous algebraic equations. It is found that the velocity profiles are generally highly dependent on the divergence parameter s, as well as the polytropic indices. Numerical results are given for a variety of cases most relevant to the solar corona. As s increases from 2, the value appropriate to purely spherically symmetric expansion, the outflow velocity increases throughout the range from the coronal base out to infinity, over a certain parameter range. Although the terminal outflow speed for s > 2 may be far in excess of the purely spherically symmetric value, we find that high speed streams emanating from coronal holes cannot be accounted for by geometrical effects alone. The results may have important applications in the general theory of stellar winds.