A reservoir has been constructed to supply irrigation water toadjacent farmland.

Question

A reservoir has been constructed to supply irrigation water toadjacent farmland. The water requirement for the farmland iscomposed of water lost by evaporation (10,000 m3/yr) andthe water needed to flush out the salt carried in the irrigationwater. The salty return water is called agricultural returnflow, and the salt concentration can not exceed 3,000g/m3, otherwise plants are killed. If theagricultural return flow enters the resevoir as indicated in thedefinition sketch, determine: (a) the water flow rate out of thereservoir; (b) the salt concentration leaving the resrvoir; and (c)the pumping rate needed to irrigate the farmland and flush saltsback into the reservoir. Assume steady state conditionsapply, no rainfall, no reservoir evaporation, and no salt lost byevaporation.

Explanation / Answer

Assuming q1,c1 and q2,c2 as the respective input andoutput parameters of water flow and salt conc. to thefarmland Reservior    --------q1, c1------->   farmland --------> 10000 m3/yr                   <-------q2,c2--------- Now since Steady state condition holds then for the reservoir with constant volume the algebraic sum ofall flows = 0 Qin - Qo - q1 + q2 =0                  ------------------------1 and similarly for the farmland total waterflow q1 - 10000 -q2 = 0 or    q1-q2 = 10,000m3/yr              ------------------------------2 putting eq 2 in 1 we get Qin - Qo - (q1-q2) = 0 or Qin - Qo - 10,000.=0 or Qin - Qo = 10,000 or Qo = Qin - 10000 = 10,000 m3/yr Also the total mass flow of salts should be constant. Soassuming the exterme case when the conc of salt in the agriculturalreturn flow is equal to 3000 gm/m3. The conc of the salt in reservoir = conc of salt in waterleaving the reservoir thus Co = c1 having said that c1 q1 - c2 q2 = 0 and Qin Cin - c1q1 + c2q2 - Qo Co = 0 or Qin Cin = Qo Co or Co = (QinCin)/Qo = 20,000* 500 / 10,000 = 1000gm/m3 now since q1c1 - q2c2 = 0 q1 Co - (q1-10,000) c2 = 0 or q1 * 1000 - (q1 -10000) 3000 = 0 or q1 = 10,000*3000/2000 = 15,000 m3/yr ans : a) 10,000 m3/yr b) 1000 gm/yr c) 15,000 m3/yr

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