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# unsat7 - Unsaturated Flow Derivation of Governing Equations...

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Unsaturated Flow Derivation of Governing Equations Description of Mass Balance Consideration Derivation of governing differential equation is obtained by considering a volumetric element. The statement of mass balance is: The difference between the total flux into the element and the total flux out of the element is equal to the rate of change of volumetric water content. The expression for mass balance is ) 1 ( dt d z q y q x q z y x θ = Assuming D’arcy’s Law ) 2 ( s H k q = Where H z h + = Unsat7-1

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Derivation of Flow Equation Substituting Eqn. 1 into 2 yields dt d z H k z y H k y x H k x z y x θ θ θ θ = + + ) ( ) ( ) ( The equation for one-dimensional flow can be written as ) 4 ( ) ( t z H k z z = θ θ Rewriting Eqn. 4 ) 5 ( 1 ) ( t z h k z z = +
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unsat7 - Unsaturated Flow Derivation of Governing Equations...

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