Horton Model AND Philip’S Equation PDF

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Topic: HORTON MODEL AND PHILIP’S EQUATIONHORTON’S MODELNamed after Robert E. Horton, Horton's equation is a viable option when measuring ground infiltration rates or volumes. It is an empirical formula that says that infiltration starts at a constant rate, and is decreasing exponentially with time. ...

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Topic: HORTON MODEL AND PHILIP’S EQUATION HORTON’S MODEL Named after Robert E. Horton, Horton's equation is a viable option when measuring ground infiltration rates or volumes. It is an empirical formula that says that infiltration starts at a constant rate, and is decreasing exponentially with time. After some time when the soil saturation level reaches a certain value, the rate of infiltration will level off to the rate.

Philip two term model John Robert Philip   

Australian Civil Engineer “The Theory of Infiltration” -pioneered analytical solutions for infiltration. Presented the first analytical solution to Richard’s Equation for vertical and horizontal infiltration

Philip’s two term model is used for uniform soil with 

uniform soil-moisture content



excess water-supply rate

How did Philip come up with ptt?   

He found a solution to the flow equation in a form of an infinite series. Because of rapid convergence, the first two terms of the series are considered sufficient. Philip two-term (PTT) model is established.

Horizontal infiltration 

Cumulative (I) and instantaneous infiltration rate (i) are given by: 1

I =S t 2 1 i= S t 2

−1 2

S=S (θ0 ,θ i)



S = sorptivity or a function of initial and boundary water contents,



t= time elapsed since water application



When a sharp wetting front exists, the sorptivity may be approximated by:



S (θ0 , θi )=



(θ 0−θi )Lf √t

Lf = distance from the boundary to the wetting front.

Vertical infiltration 

solution for vertical infiltration which describes the time of dependence of cumulative infiltration as an infinite series in power of t1/2. 1

2

3

I =S t 2 + A1 t 2 + A2 t 2 +.. . 

A1, A2 = parameters dependent upon soil properties and on initial and boundary water contents



for practical purposes, the series in the previous equations are cut short, and olmy the first two terms remained:

For cumulative: 1 2

I =S t + A1 t For infiltration rate: −1

I =S t 2 + A1



A1≅

For long infiltration times when water is ponded on the soil surface, the final infiltration rate approaches K (θ S )=K S .

Ks 2



t e=

For flux-limited infiltration rate such as low intensity rainflow P, we may approximate the equivalent time to ponding te from the time at which i=P

S2 4(P−A 1)2...