Identify the rainfall–runoff empirical relation: Q = P − K[1.8 T + 32], where Q is runoff (cm), P is annual rainfall (cm), T is mean annual temperature (°C), and K is a regional constant.

Difficulty: Easy

Correct Answer: English formula

Explanation:


Introduction / Context:
Empirical runoff–rainfall relations are used for preliminary water-resources assessments when detailed hydrometric records are sparse. Recognizing common forms helps select suitable starting points for catchment studies.



Given Data / Assumptions:

  • Q = P − K[1.8T + 32], units in centimetres for P and Q; T in degrees Celsius.
  • K is a catchment-specific constant.


Concept / Approach:
The presence of the temperature term modified by 1.8T + 32 (conversion towards Fahrenheit scale) is characteristic of the English formula used historically in hydrology texts for annual runoff estimation.



Step-by-Step Identification:

Compare the given structure with known empirical forms.Note the explicit temperature component 1.8T + 32, pointing to the English formula.Select the name that matches this expression.


Verification / Alternative check:
Cross-reference with common lists of empirical relations that include Justin, Khosla, English, and Vermule forms; only the English formula uses this specific temperature conversion factor.



Why Other Options Are Wrong:
Other named formulas use different variables or structures and do not include the 1.8T + 32 term.



Common Pitfalls:
Forgetting the temperature component and confusing with simpler Q–P linear relations.



Final Answer:
English formula

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