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The salinity concentration of soil solution (Cs) is given by which of the following formulas?
(Where, C = concentration of salt in irrigation water, Q = total quantity of water applied to the soil
Cu = consumptive use of water, ρeff = useful rainfall)

  • A.\(C_{s} = C \cdot Q^{2}/ Q - (C_{u} - \rho_{eff})\)
  • B.\(C_{s} = C^{2} \cdot Q^{2}/ Q - (C_{u} - \rho_{eff})\)
  • C.\(C_{s} = C \cdot Q/ Q - (C_{u} - \rho_{eff})\)
  • D.\(C_{s} = C \cdot Q/ 2[Q - (C_{u} - \rho_{eff})]\)

Answer: C

The key gives \(C_{s} = C \cdot Q/ Q - (C_{u} - \rho_{eff})\), read as \(C_s = \frac{CQ}{Q - (C_u - \rho_{eff})}\).

The salt brought in by irrigation is \(C \times Q\). Plants and evaporation remove water but leave the salt behind; of the consumptive use \(C_u\), the part met by useful rainfall \(\rho_{eff}\) does not come from irrigation. So the water left in the soil to carry the salt is \(Q - (C_u - \rho_{eff})\), and the salt concentration of the soil solution is the salt divided by that water.

The options with \(Q^{2}\) or \(C^{2}\) have no physical basis, and the form with a factor 2 in the denominator halves the true concentration.

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