A similar model of a pump is built to a ratio of 1:2. If the model pumps has the same fluid as the prototype at the same rotative speed, then the ratio of model power to prototype power input is
- A1/(2√2)
- B1/32Correct
- C1/8
- D1/(16√2)
Solution
Concept
Power scaling at the same speed
Formula
P ∝ N³D⁵
Step-by-step solution
1. Same fluid and speed: P ∝ D⁵. 2. Model/prototype = (1/2)⁵ = 1/32.
Explanation
With the same speed, the power depends only on the fifth power of the diameter.
Why the other options are wrong
The other values do not equal (1/2)⁵.
Shortcut
P ∝ D⁵ at constant N.
Correct answer: B) 1/32