V-belt compared with flat belt

Differences

Ratio of tensions in a V-belt

The belt sits in a groove whose included angle is $2\beta$ (usually 34 to 40 degrees). If $R$ is the total normal reaction from the two flanks, each flank carries a normal reaction $R_n$ with $R = 2R_n \sin\beta$. The friction on both flanks is $2\mu R_n = \dfrac{\mu R}{\sin\beta}$.

So the V-belt behaves like a flat belt with an effective coefficient of friction $\mu/\sin\beta$. Using the flat-belt derivation:

$$\frac{T_1 - T_c}{T_2 - T_c} = e^{\mu\theta/\sin\beta}$$

Why a V-belt transmits more power

For $\beta = 17^\circ$ to $20^\circ$, $\sin\beta \approx 0.3$, so the exponent is about three times larger. With $\mu = 0.3$ and $\theta = 160^\circ$ (2.79 rad), a flat belt gives $e^{0.84} = 2.3$, while a V-belt with $\beta = 20^\circ$ gives $e^{0.84/0.342} = e^{2.45} = 11.6$. A bigger ratio $T_1/T_2$ means a bigger difference in tension for the same tight-side tension, and thus more power. The belt need not be stretched so tightly, so the bearing loads are smaller.