TM-5-855-4
and that there is a progressive lag expressed in radians by
in the phase of the temperature wave.
(3) Measuring either the attenuation or the lag is sufficient to determine the diffusivity of the rock.
fundamental annual variation of 41 "F, with the approximate maximum on July 5 and minimum on
January 4. The minimum of the temperature 13 feet below ground occurs early in April or approximately
2,100 hours later. The diffusivity calculated from the attenuation (equation 3-32) is
The diffusivity calculated from the lag (equation 3-33) is
The results are within 20 percent and indicate that the diffusivity is seldom known with greater accuracy.
This fact should be remembered when the designer calculates the heat transfer to the rock.
According to equation
.0019. This very strong attenuation explains the
virtual extinction of all but the slowest variation below a certain depth. AS a result, daily surface
temperature variation is insignificant below a depth of approximately one foot but the annual
fundamental is measurable to depths exceeding 20 feet.
(5) The NBS has accumulated underground temperature data for selected stations in the
contiguous United States (NBS Report 9493, January 1968) and beneath five different surfaces (NBS Report
10373, February 1971).
(6) The integrated monthly average earth temperature from the surface to a depth of 10 feet is
insensitive to the thermal diffusivity as long as it is larger than 0.02 ft 2 /h, a condition that is normally
satisfied. The ASHRAE Handbook, Application tabulates the annual maximum and minimum of the
rock temperature average of the top 10 feet below the surface for 47 stations throughout the United States.
(7) When the proximity of a nonthermal water table must be taken into account, the designer may
estimate the water temperature of wells 30 to 60 feet below the surface at about 3 F above the mean annual
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