According to the provided affinity laws, how do Q, H, and P change with a diameter increase by a factor D at constant speed?

• A. Q doubles, H unchanged, P increases by 32 times
• B. Q doubles, H doubles, P doubles
• C. Q unchanged, H unchanged, P doubles
• D. Q ∝ D, H ∝ D^2, P ∝ D

Answer: (A)

When you scale a pump or fan by diameter while keeping rotational speed fixed, you follow the affinity laws: the flow rate grows with the cube of the diameter factor, the head grows with the square of the diameter factor, and the power grows with the fifth power. Intuitively, flow is tied to the size of the flow passage in all three spatial directions, so increasing diameter scales Q as D^3. The head reflects the energy imparted, which in these machines increases roughly with the square of the characteristic velocity, and since velocity scales with diameter at constant speed, H scales as D^2. Power is the product of flow and head, so P scales as D^3 × D^2 = D^5. For example, doubling the diameter makes Q 8 times larger, H 4 times larger, and P 32 times larger.