A pump and its (1/4) scale model are being compared. If the ratio of the heads is 5:1, then the ratio of the power consumed by the prototype and the model is
- A100
- B3.2
- C179Correct
- D12.8
Solution
Concept
Similarity laws of pumps
Formula
H ∝ N²D²; Q ∝ N D³; P ∝ N³D⁵
Step-by-step solution
1. Dp/Dm = 4; Hp/Hm = 5. 2. (Np/Nm)² = (Hp/Hm)/(Dp/Dm)² = 5/16 ⇒ Np/Nm = 0.559. 3. Pp/Pm = (Np/Nm)³ (Dp/Dm)⁵ = 0.1746 × 1024 = 178.8 ≈ 179.
Explanation
Power scales as N³D⁵; the speed ratio follows from the head ratio.
Why the other options are wrong
100 and 12.8 and 3.2 do not follow from the similarity laws.
Shortcut
P ∝ N³D⁵ with N from H.
Common mistake
Using P ∝ H D².
Correct answer: C) 179