According to Fanning’s formula, the flood discharge (Q) in cumecs is given by
- AQ = C A2/3
- BQ = C A3/4
- CQ = C A5/6Correct
- DQ = C A7/8
Solution
Concept
Fanning's formula for flood discharge
Formula
Q = C A5/6
Step-by-step solution
1. Fanning's formula is an empirical relation used to estimate peak flood discharge from catchment area A in sq km. 2. The formula is expressed as Q = C × A5/6, where C is a regional coefficient and Q is discharge in cumecs. 3. Therefore, option C represents the correct empirical formula. Answer: C
Explanation
Fanning's formula is an empirical relation used in hydrology to estimate maximum flood discharge for a catchment. According to this formula, flood discharge Q in cumecs is calculated as C times A raised to the power of 5/6, where A is the catchment area. Thus, option C represents the correct mathematical expression.
Why the other options are wrong
A) Q = C A2/3 represents Dicken's formula for flood discharge estimation. B) Q = C A3/4 represents Ryves formula for flood discharge estimation. D) Q = C A7/8 is not the correct formula for Fanning's equation.
Shortcut
Fanning's formula power is 5/6 (Q = C A5/6).
Common mistake
Confusing Fanning's formula exponent (5/6) with Dicken's formula (3/4) or Ryves formula (2/3).
Correct answer: C) Q = C A^(5/6)