FERTIGATION
CALCULATIONS
Moshe Sne
FERTIGATION
CALCULATIONS 1
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 2
MINIMUM TANK CAPACITY
TC=FD x A
TC – Tank Capacity (l)
FD – Fertilzer Dose (l/Ha.)
A – Plot Area (Ha.)
FERTIGATION
CALCULATIONS 3
CONVERSION OF NUTRIENT AMOUNT
TO QUANTITY OF COMMERCIAL
FERTILIZER
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 4
CONVERSION OF NUTRIENT AMOUNT
TO QUANTITY OF COMMERCIAL
FERTILIZER - Example
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 5
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 6
CONVERSION OF WEIGHT OF LIQUID
FERTILIZER INTO VOLUME - Example
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 7
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 8
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 9
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 10
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 11
FERTILIZER AMOUNT PER OPERATION
AND IRRIGATION WATER QUANTITY
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 12
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 13
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 14
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
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
Sd = 1.2 (has to be measured)
Nsv = (266.7 kg + 200 kg)/1.2 = 466.7/1.2 =
388.9 L FERTIGATION
CALCULATIONS 15
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 16
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 17
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 18
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 19
REQUIRED DILUTION RATIO
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 20
REQUIRED DILUTION RATIO
Example
Fnc = 50 mg/L N
Nuc = 26.7% N = 267 g/L = 267,000 mg/L
Dr = 50 / 267,000 = 1: 5340 = 187 ml/m3
FERTIGATION
CALCULATIONS 21
FERTILIZER PUMP FLOW-RATE
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 22
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 23
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 24
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 25
EQATION 2
DETERMINATION OF MINIMUM TANK
VOLUME
Tv=Fv*A
Tv=Tank Volume (l)
Fv=Fertilizer Dose (l/ha)
A=Area (ha)
FERTIGATION
CALCULATIONS 26
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 27
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 28
EXAMPLE 4
Tv=120 l
q=120 l/h
t=4*120 l / 120 l/h=4 h
FERTIGATION
CALCULATIONS 29
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 30
EXAMPLE 5
Nw=200 kg/ha N
Nc = 21% (N in Ammonium Sulfate)
Fw =100*200 kg/ha /21 = 950 kg/ha
FERTIGATION
CALCULATIONS 31
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 32
EXAMPLE 6
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 33
EQATION 7
FERTILIZER AMOUNT FOR ONE
IRRIGATION TURN
Ft=Fw*A
Ft=Fertilizer Amount by weight per turn
(kg)
Fw=Fertilizer Dose by weight (kg/ha)
A=Fertigated Area (ha)
FERTIGATION
CALCULATIONS 34
EXAMPLE 7
Fw = 150 kg/ha
A = 0.8 ha.
Ft = 150 kg/ha.* 0.8 ha. = 120 kg per
turn
FERTIGATION
CALCULATIONS 35
EQATION 8
FERTILIZER TANK DISCHARGE
q = 4 * Tv / t
q = Tank Discharge (l/h)
Tv = Tank Volume (l)
t = Fertilization Duration (h)
FERTIGATION
CALCULATIONS 36
EXAMPLE 8
Tv = 120 l
t = 20 minute
q = 4 * 120 l / (20/60) h = 1440 l/h
FERTIGATION
CALCULATIONS 37
EQATION 9
ADJUSTMENT OF INJECTOR
DISCHARGE
q=Fcv*Q
q = Injector Discharge (l/h)
Fcv = Fertilizer Concentration: l fertilizer
solution per m3 water
Q = Irrigation Water discharge
FERTIGATION
CALCULATIONS 38
EXAMPLE 9
Fcv = 2 l / m3
Q = 15 m3 /h
q = 2 l /m3 * 15 m3 = 30 l/h
FERTIGATION
CALCULATIONS 39
EQATION 10
ADJUSTMENT OF INJECTION
DISCHRGE-QUANTITATIVE DOSING
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 40
EXAMPLE 10
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 41
EQATION 11
AMOUNT OF SOLID FERTILIZER IN
WATER UNIT
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 42
EXAMPLE 11
Nc = 90 ppm
N% = 21% N (In Ammonium Sulfate)
Fc = 100 * 90 ppm / 21 = 429 g /m3
FERTIGATION
CALCULATIONS 43
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 44
EXAMPLE 12
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 45
INJECTION RATIO
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 46
EQATION 13
DILUTION PERCENTAGE
D% = 100 * Fcv / Qr
D% = Dilution percentage (%)
Fcv = Fertilizer volumetric concentration
(l / m3)
Qr = Injection ratio (l / m3)
FERTIGATION
CALCULATIONS 47
EXAMPLE 13
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 48
EQATION 14
FERTILIZER AMOUNT FOR
FERTILIZATION TANK
Ft = Tv * D% / 100
Ft = Fertilzer amount per irrigation turn
(l or kg)
Tv = Tank volume (l)
D% = Dilution percentage (%)
FERTIGATION
CALCULATIONS 49
EXAMPLE 14
Tv = 250 l
D% = 15.4%
Ft = 250 l * 15.4 / 100 = 38.5 l fertilizer
solution
FERTIGATION
CALCULATIONS 50
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 51
TOMATOES NUTRIENT CONSUMPTION
FERTIGATION
CALCULATIONS 52
TOMATOES WATER CONSUMPTION
mm
FERTIGATION
CALCULATIONS 53
NUTRIENT ELEMENTS
DISTRIBUTION IN TOMATO PLANT
FERTIGATION
CALCULATIONS 54
