Previous studies have shown that the solar wind speed observed near Ea
rth is inversely correlated with the divergence rate of magnetic flux
tubes near the Sun. We test the global validity of this relationship b
y employing Ulysses wind speed measurements during 1990-1997 as well a
s inecliptic data for 1976-1997. When the correspondence between wind
speeds and expansion factors is adjusted to yield optimal agreement wi
th the high-latitude Ulysses measurements, the model matches the overa
ll patterns of fast and slow wind near the ecliptic but predicts too m
uch very fast wind there. We show how this discrepancy can be resolved
by taking account of wind stream interactions, where we apply a crude
algorithm based on the propagation times of neighboring wind parcels;
the interactions reduce the amount of very fast wind at latitudes whe
re slow wind is present. We also test and reject an alternative model
in which the wind speed is assumed to be a function only of angular di
stance from the heliospheric neutral sheet.