The power available from a hydropower dam is P = 9.81๐โ๐ where P is the power in kilowatts, q is the flow rate in cubic meters per second, h is the head height in meters, and ฮท is the efficiency factor. This paper claims that beaver dams have a head height from 0.3m-5m with most below 1.5m and a width up to 46m but usually 10m or less and mentions that beaver dams can withstand a flow rate of 1.34m^3/s per meter width for a dam with a height of 1.4m. So if we estimate a 75% efficiency and go with 1.34m^3/s per meter width, 10m width and 1.4m head that gives us:
P = 9.81 * 13.4 m^3/s * 1.4m * 0.75
for a power of 138kW.