1 g c I Figure 3. Solution topology of equation (5) for as < /3 < a/(a-\).the sonic point in the flow approaches the coronal base so that ^o = to -a/2 and ^0, -a [ a + 1 -2 s ( a -l ) ] / 2 ( a -l ) .A selection of results is given in Table 1 for various values of the coronal base temperature T 0 and the polytropic index a. In these calculations it has been assumed that r" = R ©, the solar radius, and that m = (proton mass)/2. A prominent feature of the results is the demonstration that the terminal velocity of the coronal stream increases as the divergence parameter of the flow tube increases, for given values of T 0 and a. This result is in accordance with observations. Adams and Sturrock (1975) used Parker's (1963) theory to construct a coronal hole model but in their model the terminal fluid velocity above a coronal hole decreases as 5 increases, which contradicts observations. A second feature illustrated in Table 1 is that, as the coronal base temperature decreases, the model accommodates a much greater terminal fluid velocity relative to its value for purely spherically symmetric flow, i.e. Max{« 00 (i)/w 00 (2) } increases, as T 0 decreases. This means that the present model is more effective at low coronal base temperatures. Thus, largely in accordance with observations, for To = 1.5 x 10 6 K the model predicts that, as the flow becomes more divergent, the initial velocity changes from 0.29 km s" 1 to approach 165 km s~' as the critical radius changes from 9.9 R Q to approach the coronal base. However, the corresponding terminal velocity approaches 437 km s"' which is rather low for a high-speed stream. We suggest that this failing in the present model may be remedied by replacing the polytropic regime by a realistic energy equation which includes the effects of waves in the lower corona, and by considering a flow tube which has a more rapidly diverging cross-section than A(r) 2 near the coronal base and 5 = 2 downstream. This would more accurately simulate a real coronal hole, though if we change the value of s downstream of the sonic point then, for instance, such a change would not affect the value of u x .