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IBM

Physics MCP Server

by IBM

calculate_pressure_at_depth

Calculate hydrostatic pressure at specific depths using the formula P = P_atm + ρgh. Input depth and fluid density to determine total pressure, gauge pressure, and pressure in atmospheres for applications like scuba diving or engineering.

Instructions

Calculate pressure at depth: P = P_atm + ρgh.

Hydrostatic pressure increases with depth.

Args:
    depth: Depth below surface in meters
    fluid_density: Fluid density in kg/m³ (water=1000, seawater=1025)
    atmospheric_pressure: Pressure at surface in Pascals (default 101325)
    gravity: Gravitational acceleration in m/s² (default 9.81)

Returns:
    Dict containing:
        - total_pressure: Total pressure in Pascals
        - gauge_pressure: Pressure above atmospheric in Pascals
        - pressure_atmospheres: Pressure in atmospheres (1 atm = 101325 Pa)

Example - Scuba diving at 30m:
    result = await calculate_pressure_at_depth(
        depth=30,  # meters
        fluid_density=1025,  # seawater
        atmospheric_pressure=101325
    )
    # Result: ~4 atmospheres

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
depthYes
fluid_densityYes
atmospheric_pressureNo
gravityNo
Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations provided, the description carries full burden and does well by specifying the calculation method, default values for atmospheric_pressure and gravity, and the return format (dictionary with three pressure values). It clearly indicates this is a pure calculation tool with no side effects, though it doesn't mention error handling or input validation.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Well-structured with formula, conceptual explanation, parameter details, return format, and example. The information is front-loaded with the core purpose. Slightly verbose with the detailed example, but every section adds value for understanding this calculation tool.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a calculation tool with no annotations and no output schema, the description provides excellent coverage: purpose, formula, parameter details with units and defaults, return format, and a practical example. The only minor gap is lack of explicit error cases or boundary conditions.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters5/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

With 0% schema description coverage, the description fully compensates by providing detailed parameter semantics: units (meters, kg/m³, Pascals, m/s²), typical values (water=1000, seawater=1025), defaults (101325, 9.81), and which parameters are required versus optional. This adds substantial meaning beyond the bare schema.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool's purpose with a specific verb ('calculate') and resource ('pressure at depth'), including the exact formula P = P_atm + ρgh. It distinguishes from siblings by focusing specifically on hydrostatic pressure calculation rather than other physics calculations like buoyancy, drag, or orbital mechanics.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines3/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description implies usage through the example (scuba diving at 30m) and mentions hydrostatic pressure increases with depth, but doesn't explicitly state when to use this tool versus alternatives like 'calculate_buoyancy' or 'simulate_underwater_motion'. No explicit when-not-to-use guidance or alternative tool recommendations are provided.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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