Fertigation Calculations 2013 [PDF]

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FERTIGATION CALCULATIONS



Moshe Sne FERTIGATION CALCULATIONS



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INJECTOR DISCHARGE     



ID=A x FD / T ID – Injector Discharge (l/h) A – Plot area (Ha.) FD – Fertilizer Dose (l/Ha.) T – Application Duration (h)



FERTIGATION CALCULATIONS



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MINIMUM TANK CAPACITY    



TC=FD x A TC – Tank Capacity (l) FD – Fertilzer Dose (l/Ha.) A – Plot Area (Ha.)



FERTIGATION CALCULATIONS



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CONVERSION OF NUTRIENT AMOUNT TO QUANTITY OF COMMERCIAL FERTILIZER 



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Qc = Quantity of commercial fertilizer (kg) Nu = Nutrient amount (kg) P% = Percentage (per weight) of the nutrient in the commercial fertilizer (%) Qc = Nu / P%



FERTIGATION CALCULATIONS



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CONVERSION OF NUTRIENT AMOUNT TO QUANTITY OF COMMERCIAL FERTILIZER - Example  



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50 kg of nitrogen (Nu) to be applied. Ammonium sulfate contains 21% of nitrogen. Qc = 50 kg / 21% = 50 / 21 x 100 = 238.1 kg (NH4)2SO4



FERTIGATION CALCULATIONS



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CONVERSION OF WEIGHT OF LIQUID FERTILIZER INTO VOLUME*     



Vc = Volume of the liquid commercial fertilizer (L) to be applied Qc = Quantity of commercial fertilizer in weight units (kg) Sd = Specific density of the liquid fertilizer (kg/L) Vc = Qc/Sd *Measuring quantities of liquid fertilizer by volume is often more convenient than by weight FERTIGATION CALCULATIONS



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CONVERSION OF WEIGHT OF LIQUID FERTILIZER INTO VOLUME - Example 



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Weight of ammonium nitrate to be applied (Qc) = 250 kg Specific density of the ammonium nitrate solution (Sd) = 1.27 kg per liter Vc = 250 kg./1.27 = 196.8 L NH-4NO3



FERTIGATION CALCULATIONS



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COMBINATION OF TWO FERTILIZERS Simultaneous application of two or more nutrients requires mixing two or more commercial fertilizers         



Qa = Quantity of fertilizer a (kg) to be applied Qb = Quantity of fertilizer b (kg) to be applied Nu1 = Quantity of nutrient 1 (kg) to be applied Nu2 = Quantity of nutrient 2 (kg) to be applied Nu1a% = Concentration of nutrient 1 in fertilizer a (% weight) Nu2a% = Concentration of nutrient 2 in fertilizer a (% weight) Nu2b% = Concentration of nutrient 2 in fertilizer b (% weight) Qa = Nu2/ Nu2a% Qb = (Nu1 – Qa x Nu1a%)/Nu1b% FERTIGATION CALCULATIONS



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COMBINATION OF TWO FERTILIZERS Example           



Nu1 = 50 kg N Nu2 = 50 kg K2O Fertilizer a = KNO3 (13-0-46): Nu1a% = 13 (13% N) Nu2a% = 46 (46% K2O) Qa = 50kg/46% (50/46 x 100) = 108.7 kg. That amount of KNO3 contains: Nu1a (N) = 108.7 kg x 13% = 14.1 kg. N Nu1b (N) needed in the complementary fertilizer = 50 kg – 14.1 kg = 35.9 kg. Fertilizer b = NH4NO3 (21-0-0) Qb = 35.9 kg/21% = 35.9 / 21 x 100 = 170.8 kg. FERTIGATION CALCULATIONS



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FERTILIZER AMOUNT PER OPERATION AND AREA    



Qfo = Fertilizer amount per operation (kg) Qfa = Fertilizer amount per area units (kg) Au = Number of area units irrigated (ha) Qfo = Au x Qfa



FERTIGATION CALCULATIONS



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FERTILIZER AMOUNT PER OPERATION AND AREA-Example   



Qfa = 200 kg/ha Au = 15 ha Qfo = 15 ha x 200 kg/ha = 3000 kg



FERTIGATION CALCULATIONS



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FERTILIZER AMOUNT PER OPERATION AND IRRIGATION WATER QUANTITY 



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Qfo = Fertilizer amount per operation (kg) Qwa = Irrigation water amount (m3/ha) Fcw = Fertilizer concentration in irrigation water (mg/L) Au = Number of area units irrigated (ha) Qfo = Au x Qwa x Fcw FERTIGATION CALCULATIONS



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FERTILIZER AMOUNT PER OPERATION AND IRRIGATION WATER QUANTITY Example    



Qwa = 300 m3/ha Fcw = 200 mg/L = 200 g/m3 = 0.2 kg/m3 Au = 15 ha Qwa = 15 ha x 300 m3/ha x 0.2 kg/m3 = 900 kg.



FERTIGATION CALCULATIONS



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NUTRIENT SOLUTION VOLUME       



Nsv = Nutrient solution volume (L) Fs% = Fertilizer solubility at the relevant temperature (% w/v) Qf = Fertilizer amount to be applied (kg) Wv = Minimal water volume needed for dissolution of the given amount of fertilizer (l) Ww = Weight of Wv (kg) Sd = Specific density of the solution (kg/L) Nsv = (Qf/Fs%+Qf)/Sd FERTIGATION CALCULATIONS



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NUTRIENT SOLUTION VOLUME Example    



Qf = 200 kg (NH4)2SO4 Fs% (NH4)2SO4 at 200 C = 750 g/L Wv = 200 kg/75% = 200/75 x 100 = 266.7 L Ww = 266.7 kg



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In the dissolution process the volume of the solution will be smaller than the total volume of the fertilizer and the water. The actual volume will be determined by measurement of the specific density of the solution



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Sd = 1.2 (has to be measured) Nsv = (266.7 kg + 200 kg)/1.2 = 466.7/1.2 = 388.9 L FERTIGATION



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CALCULATIONS



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NUTRIENT CONCENTRATION IN NUTRIENT SOLUTION, PER WEIGHT      



Nus% = Nutrient concentration in the nutrient solution (%) Qf = Fertilizer quantity (kg) Nu% = w/w percentage of the nutrient in the fertilizer (%) Nsv = Volume of the nutrient solution (L) Sd = Specific density of the fertilizer solution (kg/L) Nus% = Qf x Nu%/(Nsv x Sd) FERTIGATION CALCULATIONS



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NUTRIENT CONCENTRATION IN NUTRIENT SOLUTION, PER WEIGHT Example     



Qf = 200 kg. Nu% = 61% Nsv = 500 Sd = 1.12 Nus% = 200kg x 61%/(500 x 1.12)= 200 x 61/100 / (500 x 1.12) =21.8% FERTIGATION CALCULATIONS



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NUTRIENT CONCENTRATION IN NUTRIENT SOLUTION, PER VOLUME     



Nus% = Nutrient concentration in the nutrient solution (%) Qf = Fertilizer quantity (kg) Nu% = w/w percentage of the nutrient in the fertilizer (%) Nsv = Volume of the nutrient solution (L) Nus% = Qf x Nu%/Nsv FERTIGATION CALCULATIONS



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NUTRIENT CONCENTRATION IN NUTRIENT SOLUTION, PER VOLUME Example    



Qf = 200 kg. Nu% = 61% Nsv = 500 Nus% = 200kg x 61%/500 = 200 x 61/100 / 500 = 24.4%



FERTIGATION CALCULATIONS



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REQUIRED DILUTION RATIO 



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The required dilution ratio is calculated for adjusting the ratio between the quantity of irrigation water applied and the amount of the injected fertilizer solution Dr = Dilution ratio Fnc = Final nutrient concentration in irrigation water w/v (mg/L) Nuc = Nutrient concentration in fertilizer stock solution w/v (%)



Dr = Fnc/Nuc FERTIGATION CALCULATIONS



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REQUIRED DILUTION RATIO Example



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Fnc = 50 mg/L N Nuc = 26.7% N = 267 g/L = 267,000 mg/L



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Dr = 50 / 267,000 = 1: 5340 = 187 ml/m3



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FERTIGATION CALCULATIONS



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FERTILIZER PUMP FLOW-RATE 



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Calculation of the flow-rate of fertilizer pumps is needed for the selection of the appropriate pump and for the adjustment of the pump flow-rate in the field, manually or by the irrigation controller Pfr = Pump flow-rate (L/h) Fnc = Final nutrient concentration in irrigation water w/v (mg/L) Nuc = Nutrient concentration in fertilizer stock solution w/v (%) Wfr = Irrigation water flow-rate (m3/h) Pfr = Wfr x Fnc / Nuc FERTIGATION CALCULATIONS



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FERTILIZER PUMP FLOW-RATE Example    



Wfr = 80 m3 Fnc = 50 mg/L Nuc = 26.7% Pfr =80 m3/h x 50 mg/l /26.7% =80.000 l x 50 mg/l /267,000 mg/l=14.5 l/h



FERTIGATION CALCULATIONS



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EQATION 1 DETERMINATION OF INJECTION RATE



    



q=A* Fv/t q= Injection rate (l/h) A=Area (Ha) Fv=Fertilizer dose (l/Ha) t=Fertilization Duration (h)



FERTIGATION CALCULATIONS



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EXAMPLE 1    



Fv - the Fertilizer Dose = 150 l/ha. A - Area = 2.5 ha. t - Fertilization Duration = 3 h. q=2.5 Ha * 150 l/Ha/ 3 h = 125 l/h



FERTIGATION CALCULATIONS



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EQATION 2 DETERMINATION OF MINIMUM TANK VOLUME    



Tv=Fv*A Tv=Tank Volume (l) Fv=Fertilizer Dose (l/ha) A=Area (ha)



FERTIGATION CALCULATIONS



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EXAMPLE 2   



Fv - the Fertilizer Dose = 200 l/ha A - Area 0.5 ha min Tv = 200 l/ha * 0.5 ha = 100 l



FERTIGATION CALCULATIONS



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EQATION 4 DETERMINATION OF FERTILIZATION DURATION    



t=4*Tv/q t=Fertilization Duration (h) Tv=Tank Volume (l) q=Tank Discharge (l/h)



FERTIGATION CALCULATIONS



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EXAMPLE 4



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Tv=120 l q=120 l/h t=4*120 l / 120 l/h=4 h



FERTIGATION CALCULATIONS



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EQATION 5 CONVERSION OF NUTRIENT AMOUNT TO FERTILIZER AMOUNT    



Fw=100 * Nw / Nc(%) Fw=Fertilizer Dose by weight kg/Ha Nw=Nutrient Dose by weight kg/Ha Nc=Nutrient concentration by weight (%)



FERTIGATION CALCULATIONS



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EXAMPLE 5



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Nw=200 kg/ha N Nc = 21% (N in Ammonium Sulfate) Fw =100*200 kg/ha /21 = 950 kg/ha



FERTIGATION CALCULATIONS



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EQATION 6 CONVERSION OF AMOUNT BY WEIGHT TO VOLUME    



Fv = Fw / Sw Fv=Fertilizer Dose by volume Fw=Fertilizer Dose by weight Sw= Specific Weight of the commercial fertilizer (kg/l)



FERTIGATION CALCULATIONS



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EXAMPLE 6



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Fw=65 kg/ha liquid Ammonium Nitrate Sw=1.27 kg/l Fv = 65 kg/ha /1.27 kg/l = 51.18 l/ha



FERTIGATION CALCULATIONS



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EQATION 7 FERTILIZER AMOUNT FOR ONE IRRIGATION TURN  



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Ft=Fw*A Ft=Fertilizer Amount by weight per turn (kg) Fw=Fertilizer Dose by weight (kg/ha) A=Fertigated Area (ha)



FERTIGATION CALCULATIONS



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EXAMPLE 7



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Fw = 150 kg/ha A = 0.8 ha. Ft = 150 kg/ha.* 0.8 ha. = 120 kg per turn



FERTIGATION CALCULATIONS



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EQATION 8 FERTILIZER TANK DISCHARGE



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q = 4 * Tv / t q = Tank Discharge (l/h) Tv = Tank Volume (l) t = Fertilization Duration (h)



FERTIGATION CALCULATIONS



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EXAMPLE 8



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Tv = 120 l t = 20 minute q = 4 * 120 l / (20/60) h = 1440 l/h



FERTIGATION CALCULATIONS



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EQATION 9 ADJUSTMENT OF INJECTOR DISCHARGE   



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q=Fcv*Q q = Injector Discharge (l/h) Fcv = Fertilizer Concentration: l fertilizer solution per m3 water Q = Irrigation Water discharge



FERTIGATION CALCULATIONS



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EXAMPLE 9



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Fcv = 2 l / m3 Q = 15 m3 /h q = 2 l /m3 * 15 m3 = 30 l/h



FERTIGATION CALCULATIONS



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EQATION 10 ADJUSTMENT OF INJECTION DISCHRGE-QUANTITATIVE DOSING     



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q = Ft / t q = Injector Discharge (l/h) Fv = Fertilizer dose (l/Ha) A = Area (Ha) Ft = Fertilizer solution amount during the irrigation turn (l) t = Fertigation Duration (h) FERTIGATION CALCULATIONS



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EXAMPLE 10



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Fv = 100 l / Ha A = 5 Ha t=5h Ft = 100 l / Ha * 5 Ha = 500 l q = 500 l / 5 h = 100 l / Ha



FERTIGATION CALCULATIONS



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EQATION 11 AMOUNT OF SOLID FERTILIZER IN WATER UNIT  



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Fc = 100*Nc / N% Fc = Fertilizer amount fer water unit (g/m3) Nc = Nutrient Concentration in Irrigation water (ppm) N% = Nutrient Concentration in the fertilizer (%) FERTIGATION CALCULATIONS



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EXAMPLE 11



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Nc = 90 ppm N% = 21% N (In Ammonium Sulfate) Fc = 100 * 90 ppm / 21 = 429 g /m3



FERTIGATION CALCULATIONS



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EQATION 12 VOLUMETRIC AMOUNT OF LIQUID FERTILIZER PER WATER UNIT     



Fcv = 100 * Ncw / Nc% *Sw Fcv = Volumetric fertilizer amount (l) per 1 m3 of water Ncw = Nutrient concentration in the irrigation water (ppm = g/m3) Nc% = Nutrient concentration in the fertilizer (%) Sw = Specific weight (density) of the fertilizer solution (g/ml) FERTIGATION CALCULATIONS



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EXAMPLE 12



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Ncw = 90 ppm N% = 21% (in Ammonium Nitrate) Sw = 1.27 g/ml Fcv = 100 * 90 ppm /(21*1.27) = 337 g/m3



FERTIGATION CALCULATIONS



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INJECTION RATIO



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Qr = q/Q Qr = Injection ratio (l injected solution per m3 irrigation water) Q = irrigation water discharge (m3/h) q = fertilizer solution discharge (l/h)



FERTIGATION CALCULATIONS



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EQATION 13 DILUTION PERCENTAGE



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D% = 100 * Fcv / Qr D% = Dilution percentage (%) Fcv = Fertilizer volumetric concentration (l / m3) Qr = Injection ratio (l / m3)



FERTIGATION CALCULATIONS



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EXAMPLE 13



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Ncw = 60 ppm N Nc% = 21% (in Ammonium Nitrate) Sw = 1.27 Q = 105 m3/h q = 150 l/h a. Fcv = 100 * 60 ppm / (21*1.27) =225 ml/m3 b. Qr = 150 l/h / 105 m3/h = 1.43 l/m3 c. D% = 100 * Fcv / Cr = 100*0.225 l/m3 /1.43 l/m3 = 15.4% FERTIGATION CALCULATIONS



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EQATION 14 FERTILIZER AMOUNT FOR FERTILIZATION TANK  



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Ft = Tv * D% / 100 Ft = Fertilzer amount per irrigation turn (l or kg) Tv = Tank volume (l) D% = Dilution percentage (%)



FERTIGATION CALCULATIONS



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EXAMPLE 14



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Tv = 250 l D% = 15.4% Ft = 250 l * 15.4 / 100 = 38.5 l fertilizer solution



FERTIGATION CALCULATIONS



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ATOMIC WEIGHTS OF NUTRITION ELEMENTS ELEMENT



ATOMIC Wt.



ELEMENT



ATOMIC Wt.



N



14



H



1



P



31



C



12



K



39.1



Fe



55.9



Ca



40.1



Zn



65.4



Mg



24.3



Mn



54.9



S



32.1



Cu



63.5



O



16



B



10.8



FERTIGATION CALCULATIONS



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TOMATOES NUTRIENT CONSUMPTION



FERTIGATION CALCULATIONS



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TOMATOES WATER CONSUMPTION mm



FERTIGATION CALCULATIONS



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NUTRIENT ELEMENTS DISTRIBUTION IN TOMATO PLANT



FERTIGATION CALCULATIONS



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