17.4.4. Empirical Formulas

Used when limited data is available. Examples include:

Empirical formulas are mathematical relationships based on observed data, often used in situations where complete information may not be accessible. They allow scientists and engineers to estimate unknown parameters, such as evaporation rates, when only limited data is at hand. This section will cover three specific empirical formulas that can be utilized, each serving different conditions.

Imagine trying to predict the dropping temperature outside based on your experiences from previous winters when you only have a few old records. Just like we use past experiences to guess future trends, empirical formulas use simplified assumptions based on previous observations to make estimations in science.

a) Meyer’s Formula E = K (es – ea) (1 + u₉)

• K = 0.36 for large deep waters, 0.50 for small shallow waters
• es, ea = saturation and actual vapor pressures
• u₉ = wind speed at 9 m height

Meyer’s Formula is used to estimate evaporation (E) from water bodies based on the difference between saturation vapor pressure (es) and actual vapor pressure (ea), adjusted by wind speed at a specific height and a constant (K) that varies depending on the body of water. Specifically, larger and deeper bodies of water will have a different K value than smaller, shallower ones. This formula captures the relationship between environmental conditions and evaporation rates, making it useful in a variety of contexts.

Think of Meyer’s Formula like a recipe for baking a cake. Just as you adjust the amount of flour depending on whether you're making a small cake or a large one, K helps adjust the formula based on water body size, allowing us to bake up an accurate estimation of evaporation!

b) Rohwer’s Equation E = (0.771 + 0.06T) (es – ea) (1 + 0.1u)

• T = air temperature in °C
• es, ea = vapor pressures
• u = wind velocity in km/hr

Rohwer’s Equation builds on the principles of Meyer’s Formula, incorporating air temperature (T) to adjust the evaporation estimate. It accounts for both the difference in vapor pressures and the wind velocity while also factoring in the ambient temperature, which influences how much moisture can be held in the air. The equation's components help in assessing conditions that affect evaporation more holistically.

Imagine you're trying to determine how quickly a puddle will evaporate after a rain shower. If it’s warm outside (high T), the water will dry up faster, similar to how flavorful aromas are intensified when a dish is heated up. That's how Rohwer’s Equation shows the effect of temperature alongside other factors in the evaporation process.

c) Blaney–Criddle Method Used in irrigation engineering: E = p (0.46T + 8.13)

• p = mean daily percentage of annual daytime hours
• T = mean monthly temperature in °C

The Blaney–Criddle Method is particularly useful in irrigation engineering and provides a way to estimate evaporation based on mean daily percentage of annual daylight hours (p) and average monthly temperature (T). The formula emphasizes that both the amount of sunlight and temperature significantly influence evaporation, important for managing water resources in agricultural contexts.

Consider how plants need both sun and warmth to thrive, similar to how they need water to grow. The Blaney–Criddle Method quantifies this relationship, just like a farmer decides when to water based on how sunny and warm it has been. It's a tool to optimize watering efficiently in agriculture.

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