Warning!
If you calculate water depth assuming constant water density and constant gravity acceleration, you do it in a wrong way.
Take a look at this simple water depth calculator to make you estimations more precise and accurate!
Calculation of depth by a given hydrostatic pressure comes from a simple equation:
P = ρ · g · h
Where P is pressure, generated by the water column with height h and density ρ.
The depth h can be estimated as follows:
h = (P - P_{0}) / (ρ · g)
Where P_{0} - is the atmospheric pressure above the water surface.
But neither ρ nor g is constants.
As well as the atmospheric pressure P_{0} - which in some cases can vary hourly.
Gravity constant g in the simple case is a function of geographic latitude.
Since the Earth rotates around an axis going through north and south poles, the gravity force is
lower on equator due to centrifugal forces and higher on poles.
To estimate the adequate value of gravity acceleration we can use the WGS84 gravity formula
^{[1]}^{[2]}.
In real-world applications water density ρ is a function of water
temperature t, salinity s and pressure P.
Its value can be estimated according to the UNESCO equation^{[3]}.
Parameter | Notation | Value | Range | Units |
---|---|---|---|---|
Water temperature | t | -4 .. 40 | °C | |
Atmosperic pressure | P_{0} | 870 .. 1090 | mBar | |
Hydrostatic pressure | P | 10^{3} .. 10^{6} | mBar | |
Geographic latitude | φ | -90 .. 90 | ° | |
Water salinity | s | 0 .. 42 | PSU |
Parameter | Notation | Value | Units | Description |
---|---|---|---|---|
Water density | ρ | kg/m^{3} | For the point with given P and t | |
Gravity acceleration | g | m/s^{2} | For the specified φ | |
Depth | h_{swg} | m | For ρ=1023.6^{[4]} kg/m^{3}, g=9.80665^{[5]} m/s^{2} | |
Depth | h_{sw} | m | For ρ=1023.6^{[4]} kg/m^{3}, g=g(φ) | |
Depth | h_{fwg} | m | For ρ=998.02^{[6]} kg/m^{3}, g=9.80665^{[5]} m/s^{2} | |
Depth | h_{fw} | m | For ρ=998.02^{[6]} kg/m^{3}, g=g(φ) | |
Depth | h_{ρP0} | m | ρ=ρ(t,P_{0},s), g=g(φ) | |
Depth | h_{ρP} | m | ρ=ρ(t,P,s), g=g(φ) | |
Depth | h_{ρPm} | m | ρ=ρ_{m}=ρ(t,(P+P_{0})/2,s), g=g(φ) |
It this calculation we assume that h_{ρPm} is the most precise value. Since the density of water ρ depends on pressure P almost linearly, we try to take into account the compressibility of water by calculating water density for the midpoint ρ_{m}=ρ(t,(P+P_{0})/2,s).
Parameter | Notation | Value | Range | Units |
---|---|---|---|---|
Number of pressure intervals | N_{p} | 2 .. 99999 |
Parameter | Notation | Value | Units | Description |
---|---|---|---|---|
Gravity acceleration | g | m/s^{2} | For the specified φ | |
Depth | h_{ρP0} | m | ρ=ρ(t,P_{0},s), g=g(φ) | |
Depth | h_{ρP} | m | ρ=ρ(t,P,s), g=g(φ) | |
Depth | h_{ρPm} | m | ρ=ρ_{m}=ρ(t,(P+P_{0})/2,s), g=g(φ) | |
Depth | h_{ρ} | m | h = (ΔP / g) · ∑ [1 / ρ(t, P_{0} + ΔPi), s], i=1..N_{p}, g=g(φ) |
It this calculation we assume that h_{ρ} is the most precise value.
To perform this calculation we take all the parameters from tables 1. and 3. Also, we need a measured temperature and salinity profile. TS-Profile is the number of measurements of temperature and salinity made in different depths.
Parameter | Notation | Value | Units |
---|---|---|---|
Number of points | N_{tsp} | ||
Z coordinate step | Z_{s} | m |
Notation | Value | Units | Description |
---|---|---|---|
h_{ts} | m | h = (ΔP / g) · ∑ [1 / ρ(t, P_{0} + ΔPi), s], i=1..N_{p}, g=g(φ), t=t(z), s=s(z) |
This calculator is made with UCNLPhysics free and open source library.