Aquaculture Formulas: The Secret Math Behind Fish Farming in AU | ORBITECH

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Stocking Density

Formulas to determine the optimal number of fish per unit area in a fish farm.

Stocking Density Formula definition

D = \frac{N}{A}

Symbol	Meaning	Unit
`D`	Stocking density Optimal stocking density ensures fish have enough space to grow.	fish/m²
`N`	Number of fish Number of fish in the aquaculture system.	fish
`A`	Area Area of the fish farm.	m²

Dimensions: $[L^{- 2}]$

Example: For a fish farm in Sydney Harbour with 5000 fish and an area of 1000 m², the stocking density is 5 fish/m².

Feed Conversion Ratio definition

F C R = \frac{F}{W}

Symbol	Meaning	Unit
`FCR`	Feed Conversion Ratio Lower FCR indicates more efficient feed use.	kg/kg
`F`	Feed given Total feed provided to the fish.	kg
`W`	Weight gain Increase in fish weight over a period.	kg

Dimensions: $[M^{0}] [L^{0}] [T^{0}]$

Example: If a barramundi farm in Queensland gives 1000 kg of feed and the fish gain 200 kg, the FCR is 5.

Specific Growth Rate definition

S G R = \frac{(\ln W_{f} - \ln W_{i})}{t}

Symbol	Meaning	Unit
`SGR`	Specific Growth Rate Measures the growth rate of fish over time.	%/day
$W_{f}$	Final weight Weight of the fish at the end of the period.	kg
$W_{i}$	Initial weight Weight of the fish at the start of the period.	kg
`t`	Time Duration of the growth period.	days

Dimensions: $[T^{- 1}]$

Example: For a fish farm in Victoria, if the initial weight of fish is 0.5 kg and the final weight is 1 kg over 30 days, the SGR is approximately 0.73%/day.

Biomass Formula definition

B = N \times W

Symbol	Meaning	Unit
`B`	Biomass Total weight of fish in the system.	kg
`N`	Number of fish Total number of fish in the system.	fish
`W`	Average weight Average weight of the fish.	kg

Dimensions: $[M]$

Example: In a fish farm in Western Australia with 1000 fish and an average weight of 0.5 kg, the biomass is 500 kg.

Water Quality

Formulas to monitor and maintain water quality in aquaculture systems.

Dissolved Oxygen Formula definition

D O = \frac{C}{V}

Symbol	Meaning	Unit
`DO`	Dissolved Oxygen Critical for fish respiration.	mg/L
`C`	Amount of oxygen Total oxygen in the water.	mg
`V`	Volume of water Volume of the water in the system.	L

Dimensions: $[M] [L^{- 3}]$

Example: For a fish farm in South Australia with 100 mg of oxygen in 50 L of water, the dissolved oxygen is 2 mg/L.

pH Formula definition

p H = - \log [H^{+}]

Symbol	Meaning	Unit
`pH`	pH level Measures the acidity or alkalinity of water.
$[H^{+}]$	Hydrogen ion concentration Concentration of hydrogen ions in the water.	mol/L

Dimensions: $[M^{0}] [L^{0}] [T^{0}]$

Example: If the hydrogen ion concentration in a fish farm in Tasmania is 10^{-7} mol/L, the pH is 7.

Salinity Formula definition

S = \frac{W_{s}}{W_{w}} \times 1000

Symbol	Meaning	Unit
`S`	Salinity Measures the salt content in water.	ppt
$W_{s}$	Weight of salts Total weight of salts in the water.	g
$W_{w}$	Weight of water Total weight of water in the system.	kg

Dimensions: $[M^{0}] [L^{0}] [T^{0}]$

Example: For a fish farm in the Great Barrier Reef with 35 g of salts in 1 kg of water, the salinity is 35 ppt.

Growth and Yield

Formulas to calculate the growth and yield of fish in aquaculture systems.

Growth Rate Formula definition

G R = \frac{W_{f} - W_{i}}{t}

Symbol	Meaning	Unit
`GR`	Growth Rate Measures the rate of fish growth over time.	kg/day
$W_{f}$	Final weight Weight of the fish at the end of the period.	kg
$W_{i}$	Initial weight Weight of the fish at the start of the period.	kg
`t`	Time Duration of the growth period.	days

Dimensions: $[M] [T^{- 1}]$

Example: For a fish farm in New South Wales, if the initial weight of fish is 0.5 kg and the final weight is 1 kg over 30 days, the growth rate is approximately 0.017 kg/day.

Yield Formula definition

Y = N \times W

Symbol	Meaning	Unit
`Y`	Yield Total yield of fish from the system.	kg
`N`	Number of fish Total number of fish in the system.	fish
`W`	Average weight Average weight of the fish.	kg

Dimensions: $[M]$

Example: In a fish farm in Queensland with 1000 fish and an average weight of 0.5 kg, the yield is 500 kg.

Survival Rate Formula definition

S R = \frac{N_{f}}{N_{i}} \times 100

Symbol	Meaning	Unit
`SR`	Survival Rate Measures the percentage of fish that survive over a period.	%
$N_{f}$	Final number of fish Number of fish at the end of the period.	fish
$N_{i}$	Initial number of fish Number of fish at the start of the period.	fish

Dimensions: $[M^{0}] [L^{0}] [T^{0}]$

Example: For a fish farm in Victoria with 1000 initial fish and 900 final fish, the survival rate is 90%.

Sources

Content derived from Wikipedia is used under CC-BY-SA 4.0. Authorship: Wikipedia contributors.