According to fan law, how many times more power is required to develop twice the volume?

When considering fan laws, specifically in relation to how power requirements change when modifying the volume flow rate of air, the third fan law is particularly relevant. This law states that the power required by a fan is proportional to the cube of the change in flow rate. Therefore, if the volume flow rate is doubled, the power requirement increases by a factor of two raised to the power of three.

To break it down, if the initial volume is represented as "V," doubling it would result in "2V." The power needed to move air at "V" is represented as P. When the volume is doubled, the new power requirement becomes:

P(new) = (2)^3 * P = 8 * P

This indicates that when the flow rate is increased to twice its original value, the power required is indeed eight times greater than the original power. This is why the correct answer is that eight times more power is required to develop twice the volume, conforming to the cubic relationship defined by fan laws.