As you sink deeper and deeper into a body of water, the amount of water pressing down on you increases. The lower you sink, the more pressure you experience. This relationship between pressure and depth is what makes calculating water depth possible. In fact, the pressure at depth and the pressure on the surface is proportional to the depth by a factor equal to the specific weight of the water. To solve for water depth, you need to know the barometric pressure, the pressure at depth and the specific gravity of water.
The derivation of this method uses some simplifying assumptions. While it is good enough for most general uses, it may not have the accuracy necessary for many laboratory or experimental applications.
Determine the atmospheric pressure (p0). You can get this by using a barometer, looking the value up in an engineering/atmosphere table or assuming atmospheric pressure to be 2116 lbs/ft^2. This is the standard atmosphere value for pressure at sea level.
Determine the pressure (p) at the depth you wish to measure. If you are working an academic problem, you will have this number given to you to solve for depth. Otherwise, you will have to obtain a measurement at your unknown depth. For this example, the pressure will be 2600 lb/ft^2.
Determine the specific weight (sw) of water. Engineering charts list this number as 62.4 lb/ft^3. You can also use a hygrometer to measure specific weight directly, since specific gravity equals density times the acceleration of gravity, but that will only add more complexity for very little in gained accuracy.
Solve the pressure-depth equation for depth (d). p - p0 = (sw)d d = (p - p0)/sw
Enter the numerical values into the equation and calculate d. d = (p - p0)/sw d = (2600 - 2116)/62.4 d = 7.76 ft
- Fundamentals of Fluid Mechanics; Bruce R. Munson, et.al.; 1990