Steady infiltration from small shallow circular ponds

Abstract

R. A. Wooding's (1968) analysis of steady infiltration from a shallow circular pond is reviewed and extended. A new approximation is obtained for the total steady flow of water into the soil from ponds with small radii. The main result is the approximation F* = 4π sin2a/{aπ sin a cos a + 2a sin 2 a ln a − a3[1 + 2ψ(3/2;)]}, which is accurate to within 2% for a less than 0.4. Here F* approximates the dimensionless flow from the pond, and a is the usual dimensionless pond radius. This result may be significant to ring infiltrometers, since substantial errors in estimates for apparent soil properties result for moderate values of a if the accurate approximation F* is replaced by the well‐known approximation 4 + 2πa. The presence of a logarithmic term in this expansion indicates that flows from surface sources have a different analytic structure than those from buried sources.