22: Appendix F—Estimating Water Pressure
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Equation 3.1 (Chapter 3, p. 80) provides a convenient approximation for the calculation of water pressure in units of atmospheres from water depth in meters. Simply put, divide the depth (m) by 10 and add 1 atmosphere. Formally:
P (atm) = z (m) / 10 (m/atm) + 1 (atm)
(Eq. 3.1)
where P is water pressure, z is depth, and 1 atm represents the pressure at sea level.
At 700 feet, water pressure is equivalent to the weight of a baby elephant on every inch of a diver’s body. Credit: Shaw and Chamberlin
For example, if the water depth is 80 meters, you would first divide by 10 (m/atm). The result, 8 atm, gives the water pressure for the water alone. But we must also take into account the force of the atmosphere, 1 atm. Adding 1 atm to 8 atm gives the correct answer of 9 atm for the water pressure at 80 meters. This is a reasonable estimate of water pressure at depth.
However, other factors, especially variations in the density of seawater, may affect water pressure. To more accurately calculate water pressure (formally known as hydrostatic pressure), you may wish to use the hydrostatic equation.
P (Pa) = ρ (kg m-3) × g (m s-2) × z (m)
(Eq. A.1)
where P is water pressure in Pascals (Pa, equivalent to Newtons per m2), ρ (pronounced “row”) is the density of the fluid in kilograms per cubic meter (kg m-3), and g is the acceleration due to gravity, a constant at 9.8 m -2), and z is water depth in meters (m). Note that 1 Pa = 1 kg × m-1 × s-2 so the units work out (in case you were wondering).
The hydrostatic equation comes into play in water columns composed of layers with different densities. Physical oceanographers will use a calculus version of the equation (we’re not going there), but for instructional purposes, just imaging three layers each with a slightly different density all stacked on top of each other. To accurately determine water pressure, you would need to calculate the pressure for each layer and add them up.
Now, unless you are pursuing a degree in oceanography, physics, or engineering, it’s not likely you’ll need to be familiar with the hydrostatic equation. But having a look beneath the hood, so to speak, will give you a greater appreciation for the measurement of pressure, on which so many things in the ocean depend. Should you ever descend in a submarine, you can rest assured the people who built it had a good understanding of this equation.