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

Question

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

 

Questions:

 

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 ?

Answer 1

This problem can be solved by pluggin in the given coefficients where indcated and then substituting the Temperature and salinity for each given location.

Below I have written out the function so all you have to do is plug in the temperature and salinity, and then copy and past the expression into google. Google calendar should give the answer.

8.00969062 x 10^(-2)+5.88194023 x 10^(-2)(T)+7.97018644 x 10^(-1)(S)+-8.11465413 x 10^(-3)(T^2)+-3.25310441 x 10^(-3)(S)(T)+1.31710842 x 10^(-4)(S^2)+4.76600414 x 10^(-5)(T^3)+3.89187483 x 10^(-5)(S)(T^2)+2.87971530 x 10^(-6)(S^2)(T)+-6.11831499 x 10^(-8)(S^3)

EXAMPLE: the density of the Gulf stream is given below.

8.00969062 x 10^(-2)+5.88194023 x 10^(-2)(27.94)+7.97018644 x 10^(-1)(35.89)-8.11465413 x 10^(-3)(27.94^2)-3.25310441 x 10^(-3)(35.89)(27.94)+1.31710842 x 10^(-4)(35.89^2)+4.76600414 x 10^(-5)(27.94^3)+3.89187483 x 10^(-5)(35.89)(27.94^2)+2.87971530 x 10^(-6)(35.89^2)(27.94)-6.11831499 x 10^(-8)(35.89^3)

=23.1321390637σ

ANOTHER RESOURCE

Below is a water density calculator, but it deviates by few kg/m^3 because it also takes into account pressure. If you choose to use this tool, in order to show your answer in σ you will need to subtract 1,000 from the answer.

http://www.csgnetwork.com/water_density_calculator.html