Real Life Application
Frequency analysis plays an important role in hydraulic engineering applications such as those concerned with floods, for example in construction of Dams it is necessary to find out the probability of occurring an extreme flood.
To understand the concept with clarity it’s important to understand two things:-
2. Return Period
With the basic concept of probability we know that probability of any event is given as Favorable cases by total number of cases. Return Period also called as Recurrence Interval or Frequency (T) is the time period on an average after which peak flood discharge is likely to be equaled or exceeded.
In order to find the Return Period Plotting Position method is used, in this method the given data is arranged in decreasing order of magnitude and accordingly rank(m) is assigned to each value. The return period for any value is then calculated by following three methods:-
• California Formula
• Weibull’s Formula
• Hazens Formula
Then the probability that a particular value is equal or exceeded is then given by-
Probability=1/T, where T is the Return Period.
We make use of Binomial Event for calculating probability, Binomial even is an event which has only two possible outcomes and is suited for this analysis also as either flood can occur or flood cannot occur. We calculate the probability that a particular event (having probability p) happens exactly r times out of n trials.
The probability of Reliability and Risk is important for us considering the design of hydraulic structures.
Reliability: This is the probability that a particular flood magnitude is never equaled or exceeded in the design life of structure.
Risk: This is the probability that a particular flood magnitude is equaled or exceeded at least once in the design life of structure.