= \frac{4 \pi C}{R_e}$$ In our new model $g$ as is given by the radial part of Eq. (\[streamfn\]), and this time, using some Bessel identities, we obtain $$C_D = \frac{2 \pi}{R_e} \frac{\epsilon^2 K_2(\epsilon)}{K_0(\epsilon)}$$

![Comparison with Tritton (1959) data](tritton){width="3.0in"}

We recall now the original assumption that $\epsilon = \sqrt{\lambda}R_e^{\beta}$. If we fix $\beta = 1$ but allow $\lambda$ to vary the drag coefficient of our model is then $$C_D = 2 \pi \lambda R_e \frac{K_2(\sqrt{\lambda}R_e)}{K_0(\sqrt{\lambda}R_e)}$$ We can plot the drag coefficient from our model, assuming that $\beta = 1$, with various choices for $\lambda$, and compare the results with those of Tritton (1959), which used an $R_e$ based on the diameter. Tritton’s data has been converted by halving [*his*]{} Reynolds number. Also, in making a comparison with Fig. 8.5 of Van Dyke (1964), it appears that Van Dyke has plotted $C_D/(4 \pi)$, as otherwise it is not possible to reconcile that plot with Tritton’s data. In Figure 1 we show the data for the first three fibres used by Tritton (those that consider the lowest $R_e$) and

-   our model with $\lambda$ picked to match the MAE result, $\lambda = 1/(4 e) \sim 0.09197$;

-   our model with a least 