16.4.4.a - Mayer’s Formula
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Introduction to Mayer’s Formula
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Today, we are going to explore Mayer’s Formula, which helps us estimate evaporation. Can anyone tell me what evaporation is?
Evaporation is when water turns from liquid to vapor. I think it happens mostly with heat from the Sun.
Exactly! Now, the formula we will discuss allows us to quantify this process. The formula is E = K(e_w − e_a)(1 + u/16). Can anyone identify the terms in this equation?
I see e_w and e_a are about vapor pressures, but what exactly are they?
Great question! e_w is the saturated vapor pressure, representing the maximum moisture the air can hold at a given temperature, while e_a is the actual vapor pressure. Understanding these terms is crucial for effective estimation!
What does the 'K' mean in the formula?
'K' is a coefficient that varies by location and season, incorporating specific site conditions into our evaporation estimates.
And how does wind speed affect evaporation?
Good observation! Wind speed, denoted as 'u,' increases evaporation by removing moisture from the surface, enhancing vapor pressure gradients. Remember this as a critical component of Mayer's Formula!
To summarize, Mayer's Formula helps us estimate evaporation based on vapor pressure differences and wind speed, critical in water management.
Calculating Evaporation Using Mayer’s Formula
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Now let's apply Mayer's Formula. Suppose we have: e_w at 25°C is 3.17 kPa, e_a is 1.81 kPa, and wind speed 'u' is 4 m/s. What might E be?
First, we need to calculate (e_w − e_a). That's 3.17 - 1.81, which equals 1.36 kPa.
Correct! Now, if we set K to 1 for simplicity, what would be our next step to calculate E?
We can calculate the term (1 + u/16). For 4 m/s, that is 1 + (4/16), which equals 1.25.
Perfect! Now multiply E = 1 * 1.36 * 1.25.
That will give us E = 1.7 mm/day!
Excellent work! This process exemplifies how Mayer's Formula is employed to derive evaporation rates using empirical parameters.
Factors Influencing Mayer’s Formula Results
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Let's discuss factors that can influence the results we obtain from Mayer's Formula. What factors do you think might cause changes?
I guess variations in temperature would play a role, right?
Absolutely! Temperature changes affect vapor pressures e_w and e_a directly. Any other factors?
Wind speed certainly comes into play since it is part of the formula.
Exactly! Wind affects the evaporation rate. Increased wind speeds help disperse the saturated air above water surfaces. Can you think of any location-specific aspects that might influence K?
Maybe humidity levels in the area or seasonal changes?
Spot on! K adjusts based on local climatic conditions such as humidity and seasons. Knowing these helps refine our evaporation estimates.
In summary, factors such as temperature, wind speed, humidity, and local conditions all heavily influence the results of Mayer's Formula.
Introduction & Overview
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Quick Overview
Standard
Mayer's Formula is an empirical equation used to estimate evaporation rates by considering the difference in vapor pressures and wind speed. It is particularly useful when direct measurements are unavailable, thereby facilitating effective water resource management.
Detailed
Mayer’s Formula
Mayer's Formula is an essential empirical equation that estimates evaporation rates, represented mathematically as:
E = K(e_w − e_a)(1 + u/16)
Where:
- E is the evaporation rate in mm/day,
- e_w is the saturated vapor pressure at the water temperature,
- e_a is the actual vapor pressure of the air,
- u is the wind speed at 9 m height,
- K is a location and season-dependent coefficient.
This formula plays a critical role in the effective management of water resources, particularly in areas where direct measurements of evaporation are challenging. It incorporates both vapor pressure conditions and wind speed as influencing factors, emphasizing their combined effects on evaporation rates. As a result, the application of this formula is significant in hydrology, irrigation planning, and environmental management.
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Understanding Mayer’s Formula
Chapter 1 of 2
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Chapter Content
E=K(e −e )(1+u /16)
Detailed Explanation
Mayer’s formula is an empirical formula used to estimate the rate of evaporation (E) in millimeters per day. In this formula, there are several important components: E represents the evaporation rate, e_w is the saturated vapor pressure at the temperature of the water, and e_a is the actual vapor pressure of the air. The term u_9 represents the wind speed at a height of 9 meters, and K is a coefficient that varies depending on the location and season. By calculating these values, we can get an estimate of how much water evaporates from a body of water.
Examples & Analogies
Think of Mayer’s formula like a recipe for making a smoothie. Just as you need the right amounts of fruits (e_w), yogurt (e_a), and other ingredients (u_9, K) blended together to make your smoothie, this formula combines various factors to estimate how much water will evaporate from a lake or pond under certain conditions.
Components of Mayer’s Formula
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Chapter Content
Where:
- E = Evaporation (mm/day)
- e_w = Saturated vapor pressure at water temperature
- e_a = Actual vapor pressure of air
- u_9 = Wind speed at 9 m height
- K = Coefficient (depends on location and season)
Detailed Explanation
Each component of Mayer’s formula plays a pivotal role in determining the evaporation rate. The 'E' value indicates how much water is lost via evaporation daily. 'e_w' refers to the amount of moisture the air can hold when it's saturated, which changes with temperature. 'e_a' reflects the actual moisture present in the air, which affects how much more water can evaporate. The wind speed at 9 meters ('u_9') influences evaporation, as more wind typically increases evaporation rates. Finally, the coefficient 'K' accounts for local variations like climate and seasonal changes which can affect evaporation.
Examples & Analogies
You can liken this to a sponge. A saturated sponge (e_w) can hold maximum water, while the actual moisture it has (e_a) affects how fast it can release the water. If the sponge is put in a windy environment (u_9), it dries out faster. Similarly, depending on where you live (K), the evaporation rate will differ, just like the drying speed of a sponge will change in different conditions.
Key Concepts
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Mayer’s Formula: An empirical equation to estimate evaporation based on vapor pressures and wind speed.
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Evaporation Rate (E): The amount of water converted from liquid to vapor per day, measured in mm/day.
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Vapor Pressure: The pressure exerted by the vapor in equilibrium with its liquid, crucial for determining evaporation.
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Coefficient K: A variable that adjusts results based on local conditions and seasonal factors.
Examples & Applications
Using Mayer's Formula, if e_w is 3.17 kPa, e_a is 1.81 kPa, and wind speed (u) is 4 m/s, the estimated evaporation (E) can be calculated as 1.7 mm/day.
In a humid environment where the vapor pressure difference is minimal, the evaporation rate calculated using Mayer's Formula will typically be lower compared to a dry or windy environment.
Memory Aids
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Rhymes
For E to be true, just subtract and see, with wind speed to add, feel evaporation's glee.
Stories
Imagine a thirsty plant in a warm patch of sun. The warmer it is, and the more wind blows, the more water it loses to the sky as vapor. This is the heart of Mayer's Formula!
Memory Tools
EVAPO: E = K(e_w - e_a)(1 + u/16) - Remember E for Evaporation, K for coefficient, e_w for saturated, e_a for actual, and u for wind speed.
Acronyms
WAVE
Water (evaporation)
Air (vapor pressures)
Velocity (wind speed)
Evaluation (through K) – the essentials of estimating evaporation.
Flash Cards
Glossary
- Evaporation
The process by which water changes from liquid to vapor phase due to the absorption of energy.
- Saturated Vapor Pressure (e_w)
The maximum pressure exerted by vapor in equilibrium with its liquid phase at a given temperature.
- Actual Vapor Pressure (e_a)
The pressure exerted by the vapor present in the air at a specific moment.
- Coefficient (K)
A variable that adjusts the formula based on specific location and seasonal conditions affecting evaporation.
- Wind Speed (u)
The speed of air movement, which affects evaporation rates by altering the moisture distribution above water surfaces.
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