Laurie P.

asked • 11/29/18

Need help with calculating the densities of water please!!!

Seawater density is often reported in σ. Densities reported this way show the deviation from pure water in kg/m3. Therefore a seawater density of 25 σ indicates an actual density of 1025 kg/m3. This is done so the important density changes are easier to visualise.


The general form of the density equation is 

σ = a +bT + cS +dT2 +eST + fS2 + gT3 + hST2 + iS2T + jS3

Where σ is the density, S is salinity (in psu) and T is temperature (in °C).

The polynomial coefficients ‘a to j’ are given below as calculated by Cox et al. (1970).

a = 8.00969062 x 10-2

b = 5.88194023 x 10-2

c = 7.97018644 x 10-1

d = -8.11465413 x 10-3

e = -3.25310441 x 10-3

f = 1.31710842 x 10-4

g = 4.76600414 x 10-5

h = 3.89187483 x 10-5

i = 2.87971530 x 10-6

j = -6.11831499 x 10-8


Table 1

Location Water Temperature (°C) Water Salinity (psu)
Gulf Stream 27.94 35.89
North Atlantic Drift 17.83 35.27
Greenland Sea 8.24 34.78
NADW 4.34 34.88
AABW 0.17 34.77




What is the density of water in the Gulf Stream (in σ)?

What is the density of water in the North Atlantic Drift (in σ)?

What is the density of water in the Greenland Sea (in σ)?

What is the density of AABW (in σ)?

What is the density of NADW in σ ?

1 Expert Answer


Valerie C. answered • 04/07/20

5 (23)

Algebra Teacher with 4 years experience

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