How many times the power of the fan is required when the ventilation volume is doubled?

When the ventilation volume is doubled, the fan power required increases according to the cubic relationship of airflow to power. Fan power is proportional to the cube of the airflow rate, which means that if the ventilation volume is increased by a factor of two, the power requirement increases by a factor of two cubed.

This can be expressed mathematically as follows:

If ( Q ) is the airflow volume and ( P ) is the power, doubling the volume implies:

( P'(new) = P(original) \times (2^3) )

Where the factor of ( 2^3 ) (or 8) represents the increase in power due to doubling the airflow rate. Hence, the power required by the fan becomes eight times the original power requirement when the ventilation volume is doubled.

Therefore, the correct answer indicates that the power of the fan must be increased to eight times in order to accommodate the doubled ventilation volume.