A submarine cannot use ordinary landmarks to judge how far below the surface it is, so depth instruments are essential for safe operation. These instruments help the crew avoid the seafloor, stay within the submarine's safe pressure limits, and navigate at assigned depths. The main idea is simple: as a submarine descends, the weight of the water above it increases, so the outside water pressure rises in a predictable way.
By measuring that pressure, the submarine can calculate its depth.
Key Facts
- Water pressure increases with depth: P = P0 + ρgh.
- Gauge pressure is the pressure due to the water only: Pgauge = ρgh.
- Depth from pressure is found by rearranging the formula: h = Pgauge / (ρg).
- Seawater density is about ρ = 1025 kg/m^3, slightly higher than freshwater.
- Every 10 m of seawater adds about 1 atm of pressure, or about 101,000 Pa.
- Modern submarines use pressure transducers, depth gauges, and computer displays to convert pressure readings into depth.
Vocabulary
- Depth gauge
- A depth gauge is an instrument that shows how far below the water surface a submarine is.
- Pressure transducer
- A pressure transducer is a sensor that converts water pressure into an electrical signal.
- Hydrostatic pressure
- Hydrostatic pressure is the pressure caused by the weight of a fluid at rest.
- Gauge pressure
- Gauge pressure is the pressure measured above the surrounding atmospheric pressure.
- Seawater density
- Seawater density is the mass of seawater per unit volume and is used to calculate pressure at depth.
Common Mistakes to Avoid
- Using total pressure when the problem gives gauge pressure. Gauge pressure already excludes atmospheric pressure, so adding P0 again gives a depth that is too large.
- Forgetting that pressure increases linearly with depth. In the basic hydrostatic model, doubling the depth doubles the gauge pressure if density stays constant.
- Using freshwater density for ocean calculations. Seawater is denser than freshwater, so using 1000 kg/m^3 instead of about 1025 kg/m^3 creates a small but real error.
- Confusing depth with distance traveled along a sloping path. Depth is the vertical distance below the surface, not the length of the submarine's path through the water.
Practice Questions
- 1 A submarine is at a depth of 120 m in seawater with density 1025 kg/m^3. Calculate the gauge pressure using Pgauge = ρgh with g = 9.8 m/s^2.
- 2 A pressure sensor measures a gauge pressure of 2.46 x 10^6 Pa in seawater. Using ρ = 1025 kg/m^3 and g = 9.8 m/s^2, find the submarine's depth.
- 3 A submarine's computer display shows depth from a pressure sensor reading. Explain why the display must account for seawater density and why the same pressure reading might not correspond to exactly the same depth in all parts of the ocean.