According to the provided affinity laws, how does Q, H, and P change with a speed increase by a factor N?

• A. Q ∝ N, H ∝ N^2, P ∝ N^3
• B. Q ∝ N^2, H ∝ N, P ∝ N^2
• C. Q ∝ 1/N, H ∝ 1/N^2, P ∝ 1/N^3
• D. Q ∝ N^0, H ∝ N^0, P ∝ N^0

Answer: (A)

When speed increases by a factor N, the affinity laws tell you how the pump or fan performance scales: the flow rate grows linearly with speed, the head grows with the square of speed, and the power grows with the cube of speed.

Flow rate is essentially the volume moved per unit time, and pushing fluid faster means more fluid is moved each second, so Q ∝ N. The head is the energy per unit weight the machine can add to the fluid, which relates to velocity head; velocity scales with speed, so the head scales with the square of speed, H ∝ N^2. Power is the rate of doing work, which for a pump or fan is roughly the product of flow and head, P ∝ Q × H. Substituting the scaling for Q and H gives P ∝ N × N^2 = N^3.

So the correct relationship is Q ∝ N, H ∝ N^2, P ∝ N^3. The other options would violate the fundamental way Q, H, and P interrelate through speed (for example, not increasing with speed, or not matching P to the product of Q and H).