Does anyone know how to solve this? Thanks for any help you can provide. As illu

Question

Does anyone know how to solve this?

Thanks for any help you can provide.

As illustrated in the figure below, a river flows into a reservoir that is being used to irrigate farmland. The river inflow is Qi = 25,000 m 3/year and the salt concentration in the river is Ci = 300 gm/m3. The reservoir can be modified as being completely mixed with a uniform salt concentration. The farmland needs irrigation water to flush out salts out of the soil and for use by plants. Water used by plants is lost by evapotranspiration and the amount of this loss, QE, equals 10,000 m3/year. Salty water from the farm is returned to the reservoir. The salt concentration in the return flow is CR = 2,500 gm/m3. Determine the following: The water flow rate out of the reservoir, Qout; The salt concentration in the reservoir, which is the same as the concentration in the flow out of the reservoir, C out (since the reservoir is completely mixed): and The flow out for the irrigation water, Qirr.

Explanation / Answer

a)

By mass conservation of water.

Water coming in = water going out

In the reservoir

25000 + Qreturn = Qout + Qirr

In the farm

Qirr = 10000 + Qreturn

This gives us

Qout = 25000 - 10000 = 15000

b)

By mass conservation of salt

Salt coming in = Salt going out

Since the reservoir is uniformly mixed, Qout and Qirr both have same salt concentration and let that be x.

In the reservoir

25000*300 + Qreturn*2500 = (15000 + Qirr)*x

7500000 + (Qirr - 10000)*2500 = (15000 + Qirr)*x

In the farm

Qirr*x = Qreturn*2500

Qirr*x = (Qirr - 10000)*2500

x = (1 - 10000/Qirr)*2500

Putting this x in the reservoir salt equation and cancelling 2500 from each term

3000 + (Qirr - 10000) = (15000 + Qirr)*(1 - 10000/Qirr)

Qirr - 7000 = 5000 -150*10^6/Qirr + Qirr

Qirr = 150*10^6 / 12000 = 12500 m^3/ year

x = 500 gm / m^3

  

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