A model of reservoir is emptied in 10 minutes. If the model scale is 1:25, then the time taken by the prototype to empty itself would be
- A250 minutes
- B50 minutesCorrect
- C6250 minutes
- D2 minutes
Solution
Concept
Time scale ratio for gravity-dominated (Froude) models
Formula
Tr = √Lr (Froude law)
Step-by-step solution
1. Reservoir emptying is gravity-driven, so use Froude similarity. 2. Length scale Lr = 25 (prototype / model). 3. Time ratio Tr = √25 = 5. 4. Prototype time = 5 × 10 = 50 minutes.
Explanation
Free-surface flows such as the emptying of a reservoir are governed by gravity. In Froude similitude, time scales as the square root of the length scale, so prototype time is 5 times the model time.
Shortcut
Froude: Tr = √Lr; Vr = √Lr; Qr = Lr2.5.
Common mistake
Using the length ratio instead of its square root.
Correct answer: B) 50 minutes