⚠️ Educational Use Only — This tool is NOT intended for real dive planning. Never use this for actual dives. Always use certified dive computers, tables, and proper training.

📊 Pressure & Partial Pressure

Understanding how pressure changes with depth and affects the gases you breathe

📈 Dive Profile Terminology

Reading a Dive Profile

A dive profile is a graphical representation of your dive, showing depth over time. Understanding the basic terminology helps you communicate with other divers and interpret dive computer data effectively.

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📖 Key Terms

📖 Key Terms

Descent The phase from leaving the surface until reaching your planned depth. Recommended rate: ≤18-20 m/min.
Bottom Time Total time from beginning of descent to start of final ascent. Includes descent phase.
Maximum Depth The deepest point reached during the dive. Determines ambient pressure and gas absorption rate.
Ascent Return to surface. Rate should not exceed 9-10 m/min to prevent bubble formation.
Total Dive Time (TDT) Complete duration from leaving surface to returning. Includes descent, bottom time, and full ascent.
Deco Stop Mandatory pause at specific depth during ascent to allow safe elimination of inert gases.
Safety Stop Voluntary 3-minute pause at 3-5m during ascent to allow excess nitrogen to off-gas safely.
Surface Interval (SI) Time spent at surface between dives to off-gas nitrogen. Longer SI = more nitrogen eliminated.

🌊 Total Pressure Underwater

What Creates Pressure Underwater?

The total pressure a diver experiences underwater comes from two sources:

  • Atmospheric pressure — The weight of the air column above you. At sea level, this is approximately 1 bar (1 atm = 1.01325 bar).
  • Hydrostatic pressure — The weight of the water column above you. In seawater, this adds approximately 1 bar per 10 meters of depth.

Therefore, at 10m depth you experience 2 bar total pressure (1 atm + 1 bar water), at 20m it's 3 bar, at 30m it's 4 bar, and so on.

📍 Atmospheric Pressure at Different Altitudes

Atmospheric pressure decreases with altitude. If you dive in a mountain lake, you start with less than 1 bar at the surface:

Altitude Pressure (bar) Example Location
Sea level 1.013 Ocean, coastal lakes
300 m 0.977 Low hills
700 m 0.932 Mountain lakes
1500 m 0.845 High altitude lakes
2500 m 0.747 Lake Titicaca
3000 m 0.701 Extreme altitude diving

⚠️ Altitude diving requires special procedures and decompression adjustments.

🔬 Mathematical Formulas

Total Ambient Pressure

The total pressure at any depth is the sum of atmospheric and hydrostatic pressure:

P_{amb} = P_{atm} + P_{hydro} = P_{atm} + \rho \cdot g \cdot h

Where:

  • P_{amb} = total ambient pressure
  • P_{atm} = atmospheric pressure (≈1 bar at sea level)
  • \rho = water density (≈1025 kg/m³ for seawater)
  • g = gravitational acceleration (9.81 m/s²)
  • h = depth in meters

Simplified Formula (Sea Level)

For diving at sea level, we use the simplified formula:

P_{amb} = 1 + \frac{depth}{10} \text{ bar}

This approximation works well for recreational diving calculations.

Atmospheric Pressure vs Altitude

Atmospheric pressure decreases exponentially with altitude:

P_{atm}(h) = P_0 \cdot e^{-\frac{h}{H}}

Where:

  • P_0 = 1.01325 bar (sea level pressure)
  • h = altitude in meters
  • H ≈ 8500 m (scale height of atmosphere)

📈 Dive Profile with Total Pressure

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⛽ Gas Consumption

Why Depth Matters for Gas Supply

According to Boyle-Mariotte's Law, as pressure increases, the volume of gas decreases proportionally. Underwater, this means you breathe compressed air from your tank. At 10m depth (2 bar), each breath draws twice the amount of gas molecules compared to the surface.

This is why deeper dives consume your gas supply faster—you're breathing the same volume of air, but it contains more gas molecules due to compression.

⛽ Surface Air Consumption (SAC)

SAC rate (also called RMV - Respiratory Minute Volume) is how much gas you breathe per minute at the surface. For planning purposes, we use a typical value of 20 L/min for relaxed diving, though actual consumption varies based on exertion, stress, and individual factors.

At depth, your actual consumption is: SAC × Ambient Pressure

  • Surface (1 bar): 20 L/min
  • 10m (2 bar): 40 L/min
  • 20m (3 bar): 60 L/min
  • 30m (4 bar): 80 L/min
  • 40m (5 bar): 100 L/min
🔬 Gas Consumption Formula

Gas Consumed at Depth

The gas consumption at any depth can be calculated as:

\text{Consumption} = SAC \times P_{amb} \times t

Where:

  • SAC = Surface Air Consumption (L/min at surface)
  • P_{amb} = Ambient pressure in bar (1 + depth/10)
  • t = Time at depth (minutes)

Available Gas in Cylinder

\text{Gas Available} = V_{cylinder} \times (P_{start} - P_{reserve})

For a 12L cylinder at 200 bar with 50 bar reserve:

Available gas = 12 × (200 - 50) = 1800 liters

📈 Gas Consumption During Dive

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📊 Calculating Your Personal SAC Rate

Knowing your personal SAC rate helps you plan dives more accurately. You can calculate it from real dive data using your pressure drop, cylinder size, dive time, and average depth.

SAC Calculation Formula

SAC = \frac{\Delta P \times V_{cyl}}{t \times P_{avg}}

Where:

  • \Delta P = Pressure drop (start - end pressure in bar)
  • V_{cyl} = Cylinder volume (liters)
  • t = Dive time (minutes)
  • P_{avg} = Average ambient pressure = 1 + (avg depth / 10)

Example Calculation

After a dive you note:

  • Cylinder: 12L
  • Start pressure: 200 bar, End pressure: 80 bar → ΔP = 120 bar
  • Dive time: 45 minutes
  • Average depth: 15m → Pavg = 1 + 15/10 = 2.5 bar
SAC = \frac{120 \times 12}{45 \times 2.5} = \frac{1440}{112.5} = 12.8 \text{ L/min}

This diver has a SAC rate of 12.8 L/min — quite efficient! Typical recreational divers range from 12-25 L/min depending on fitness, experience, and conditions.

Tips for Accurate Measurement

  • Use a dive computer that logs average depth, or calculate it from your profile
  • Measure over several dives to get a reliable average
  • Note that SAC increases with exertion, cold, or stress
  • For planning, use a conservative (higher) SAC estimate

🌬️ Air Composition

What's in the Air You Breathe?

The air we breathe is a mixture of gases. Understanding this composition is fundamental to diving because each gas behaves differently under pressure. The main components are:

  • Nitrogen (N₂) — 78% — inert gas, does not participate in metabolism
  • Oxygen (O₂) — 21% — essential for life, but toxic at high partial pressures
  • Other gases — 1% — primarily Argon, CO₂, and trace gases

Breathing Gas Mixtures

Divers use different gas mixtures to manipulate the partial pressures of specific gases at depth. By changing the fraction of each gas in a mix, divers can stay within safe limits for oxygen toxicity and nitrogen narcosis:

  • Nitrox (EAN) — Increases the oxygen fraction to lower the partial pressure of nitrogen (ppN2), which reduces nitrogen loading in the tissues.
  • Trimix — Adds helium to the mix, allowing divers to lower the partial pressures of both oxygen and nitrogen to safe levels for deep diving.

⚗️ Dalton's Law of Partial Pressures

The Foundation of Dive Gas Physics

Dalton's Law states that the total pressure of a gas mixture equals the sum of the partial pressures of each component gas. The partial pressure of a gas is the pressure it would exert if it occupied the same volume alone.

Animation of gas particles (blue and red) bouncing in a container, illustrating how each gas exerts its own partial pressure

Each gas (blue, red) exerts its own pressure independently — the total pressure is the sum of all partial pressures.

🔬 Dalton's Law Formula

Total Pressure

P_{total} = P_{N_2} + P_{O_2}

Partial Pressure Calculation

pp_x = f_x \times P_{amb}

Where:

  • pp_x = partial pressure of gas x (bar)
  • f_x = fraction of gas x in the mixture (decimal, e.g., 0.21 for 21%)
  • P_{amb} = ambient pressure (bar), calculated as 1 + depth/10

Note: This is the operational formula used for MOD and gas limits throughout this section.

⚗️ Example: Air at 30 Meters

At 30 meters, the ambient pressure is 4 bar (1 + 30/10). For air:

Gas Fraction Calculation Partial Pressure
O₂ 0.21 0.21 × 4 0.84 bar
N₂ 0.79 0.79 × 4 3.16 bar

📐 Operational vs Physiological Partial Pressure

There are two common contexts for partial pressure calculations:

Operational (MOD / gas limits)

ppO_2 = F_{O_2} \times P_{amb}

Used for Maximum Operating Depth (MOD) and oxygen toxicity limits. No water vapour subtraction.

Physiological (tissue kinetics)

pp_{inert} = F_{inert} \times (P_{amb} - P_{H_2O})

When calculating alveolar gas pressures for tissue loading models, we subtract water vapour pressure because the lungs humidify inspired air:

P_{H_2O} = 0.0627 \text{ bar at 37°C}

This ~6% reduction appears in the Bühlmann equations for tissue saturation calculations. We will need this in further sections and stating it here for completeness.

⚠️ Partial Pressure Limits

🔴 Oxygen Limits (ppO₂)

Oxygen becomes toxic at elevated partial pressures. The body responds differently to various ppO₂ levels:

ppO₂ (bar) Status Notes
< 0.16 ⚫ Hypoxia Loss of consciousness, death. Minimum for survival.
0.16 – 0.50 🟢 Normal Surface breathing range.
0.50 – 1.40 🟢 Safe for diving Recommended working limit for recreational diving.
1.40 – 1.60 🟡 Caution Acceptable for decompression stops only. Limited exposure time.
> 1.60 🔴 Danger High risk of CNS oxygen toxicity (seizures).

🔬 Maximum Operating Depth (MOD)

The MOD is the deepest you can safely dive with a specific gas mix without exceeding the ppO₂ limit. It's calculated from the oxygen fraction and desired maximum ppO₂.

🔬 MOD Formula
MOD = \left(\frac{ppO_{2,max}}{f_{O_2}} - 1\right) \times 10

Where:

  • ppO_{2,max} = maximum allowed partial pressure (typically 1.4 bar)
  • f_{O_2} = oxygen fraction in the gas (decimal)

Exercises: Calculate the MOD (ppO₂ = 1.4 bar)

Gas fO₂ Calculation MOD
Air (21% O₂) 0.21
show(1.4 / 0.21 − 1) × 10
show56.7 m
EAN32 0.32
show(1.4 / 0.32 − 1) × 10
show33.8 m
EAN36 0.36
show(1.4 / 0.36 − 1) × 10
show28.9 m
EAN40 0.40
show(1.4 / 0.40 − 1) × 10
show25.0 m

💡 Notice: higher O₂ fraction → shallower MOD. More oxygen means you hit the toxicity limit sooner.

🟡 Nitrogen Limits (ppN₂) — Narcosis

Nitrogen becomes narcotic at elevated partial pressures, causing impaired judgment, euphoria, and slowed reactions—similar to alcohol intoxication.

🍸 The "Martini Rule"

A popular rule of thumb: every 10 meters of depth on air is roughly equivalent to drinking one martini on an empty stomach. At 30m, you might feel like you've had 3 martinis!

  • 10m — 1 martini
  • 20m — 2 martinis
  • 30m — 3 martinis
  • 40m — 4 martinis

Note: Individual susceptibility varies greatly. Some divers feel effects earlier, others later. Cold, stress, and fatigue increase narcosis.

ppN₂ (bar) Equivalent Depth (Air) Effects
< 2.4 < 20m Minimal effects for most divers.
2.4 – 3.2 20 – 30m Mild euphoria, slight impairment.
3.2 – 4.0 30 – 40m Noticeable impairment, reduced judgment.
> 4.0 > 40m Severe narcosis. Maximum limit for recreational diving.

Exercises: Max depth for narcosis limit

Same formula as MOD, but for nitrogen: Max depth = ((ppN₂max / fN₂) − 1) × 10

ppN₂ limit:
Gas fN₂ Calculation Max depth

💡 Nitrox pushes the narcosis limit deeper, but the oxygen MOD kicks in first — you always need to respect both limits. The actual limiting factor for EAN mixes is usually oxygen, not narcosis.

☠️ Oxygen Toxicity

Two Types of Oxygen Toxicity

Breathing oxygen at elevated partial pressures can cause two distinct types of toxicity:

Type Cause Symptoms Diving Relevance
CNS Toxicity High ppO₂ (>1.6 bar) Seizures, convulsions, tunnel vision, twitching Immediate danger, can cause drowning
Pulmonary Toxicity Prolonged exposure (ppO₂ >0.5 bar) Chest pain, coughing, breathing difficulty Relevant for long exposures, rebreathers

📊 CNS & OTU Tracking

⚠️ Symptoms of CNS Oxygen Toxicity

Remember the mnemonic VENTID-C:

  • Visual disturbances (tunnel vision)
  • Ear ringing (tinnitus)
  • Nausea
  • Twitching (especially facial muscles)
  • Irritability, anxiety
  • Dizziness
  • Convulsions (the most dangerous)

⚠️ If you experience any of these symptoms, immediately signal your buddy and begin ascending. Underwater convulsions are often fatal.

📊 Partial Pressures During Dive

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