If V is the wind velocity and F is the fetch, for F < 32 Km, what is the formula for wave height (hw) in gravity dams ?
- Ahw = 1·032 √(VF) + 0·76 + 0·27 F1/4
- Bhw = 0·032 √(VF) − 0·76 − 0·27 F1/4
- Chw = 1·032 √(VF) − 0·76 + 0·27 F1/4
- Dhw = 0·032 √(VF) + 0·76 − 0·27 F1/4Correct
Solution
Concept
Stevenson’s formula for wave height
Formula
hw = 0.032 √(VF) + 0.763 − 0.271 F1/4 (F < 32 km)
Step-by-step solution
1. For a fetch less than 32 km (Stevenson's formula): hw = 0.032√(VF) + 0.76 − 0.27 F1/4, where V is in km/h and F in km.
Explanation
Wave height is used to fix the free board of a dam. The coefficient is 0.032, not 1.032, and the fetch term is subtracted.
Why the other options are wrong
Options with 1.032 or with a minus sign on the constant 0.76 are not Stevenson's formula.
Shortcut
hw = 0.032√(VF) + 0.76 − 0.27 F1/4.
Common mistake
Adding the fetch term.
Correct answer: D) h_w = 0·032 √(VF) + 0·76 − 0·27 F^(1/4)