# 2.26. Measurement error in which of the variables in Eq.

2.26. Measurement error in which of the variables in Eq. (2.4) (air temperature, relative
humidity, or wind velocity) will yield the largest relative error in the estimated
evaporation rate? Assume the conditions of Prob. 2.25 and a 10 percent relative
measurement error for each of the variables.
2.25. What evaporation rate would be indicated by Eq. (2.4) when the reservoir water
surface is 60'F, the air temperature at 8 m is 70° F, the relative humidity is 85 percent,
and the wind velocity at 8 m is 9 mph? If the relative humidity at 8 m were only 20
percent, what would be the evaporation rate, all other factors being the same?
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Another approach to the problem of estimating lake evaporation is the
energy-balance method. This method is expressed by the equation
H- Ho-AH
E =
(2.5)
P[(1 + R)]
where H, is the total heat input to the lake including solar radiation and heat
entering with inflowing water, H, is the heat leaving the lake as reflected and back
radiation and the heat content of the outflowing water, AH is the change in heat
content of the reservoir water, p is the density of the evaporated water, à the latent
heat of vaporization, and R a ratio of the heat used for evaporation to that
transferred to the air as sensible heat. Known as Bowen's ratio, R is given by
DESCRIPTIVE HYDROLOGY 29
simple empirical equations such as
E = 0.00241(p,, - Pu)Vs
(2.4)
were as satisfactory as the theoretical equations. In Eq. (2.4), E is evaporation in
inches per day, Po, is the vapor pressure (inches of mercury) at the water surface,
and
and Vs are the vapor pressure and the wind velocity (miles per day) 8 m
Pe
above the surface. The terms V and p, must be measured carefully; otherwise large
errors will result. With vapor pressure in millibars,' wind speed in meters per
second, and evaporation in millimeters per day, the constant in Eq. (2.4) becomes
0.097.
Another approach to the problem of estimating lake evaporation is the
vnressed by the equation