Final answer:
The power consumption is proportional to the square of the speed of rotation. If the impeller diameter is doubled, the power would be expected to increase by a factor of 4.
Step-by-step explanation:
The power consumption is found experimentally to be proportional to the square of the speed of rotation. This means that if the speed of rotation is doubled, the power would increase by a factor of four.
Let's assume the power consumption is represented by P and speed of rotation by S. Based on the given information, we can write the equation as P = kS², where k is the constant of proportionality. If the impeller diameter is doubled, the speed of rotation will also double. Therefore, the power consumption will be multiplied by (2)², which is 4. Hence, the power would be expected to increase by a factor of 4 if the impeller diameter was doubled.