No, doubling the speed of a turbine does not necessarily result in doubling the power. The power generated by a turbine depends on various factors, including the speed and the torque (rotational force) applied to the turbine.
The power output of a turbine can be calculated using the equation:
Power = Torque x Angular velocity
where torque is the rotational force applied to the turbine and angular velocity is the rotational speed in radians per second.
If the speed of a turbine is doubled while the torque remains constant, the power will increase by a factor of two. However, in practice, changing the speed of a turbine without adjusting other parameters is unlikely to keep the torque constant.
In most cases, increasing the speed of a turbine will require an increase in the torque as well to maintain efficient operation. The power output of the turbine will depend on how the torque and speed are adjusted together. Therefore, simply doubling the speed of a turbine does not guarantee that the power output will double. It would require a combination of factors, including adjustments to the torque, to determine the resulting power output accurately.