#MoonFluid - Fluid Mechanics Calculation Library

#Features

#Fluid Statics

• Hydrostatic Pressure: Pressure calculation in static fluids (p = p₀ + ρgh)
• Buoyant Force: Buoyancy calculations (F_b = ρgV)
• Total Pressure: Pressure on submerged surfaces
• Pressure Center: Center of pressure on submerged planes
• Manometry: Fluid pressure measurement calculations

#Continuity and Bernoulli

• Continuity Equation: Mass and volume flow rate conservation (Q = A₁v₁ = A₂v₂)
• Bernoulli Equation: Energy conservation in fluid flow (p/ρg + v²/2g + z = constant)
• Energy Head: Total head calculations in flow systems
• Velocity Head: Kinetic energy head calculations

#Flow Characteristics

• Reynolds Number: Flow regime classification (Re = ρvD/μ)
• Flow Regime Analysis: Laminar vs turbulent flow determination
• Froude Number: Open channel flow regime analysis (Fr = v/√(gh))
• Critical Flow: Critical flow conditions and analysis

#Pipe Flow

• Laminar Flow: Hagen-Poiseuille flow calculations
• Turbulent Flow: Darcy-Weisbach friction loss calculations
• Local Losses: Sudden expansion, contraction, and fitting losses
• Total Head Loss: Combined friction and local losses
• Pipe Sizing: Flow rate and diameter calculations

#Open Channel Flow

• Manning Equation: Open channel flow calculations
• Hydraulic Radius: Channel geometry calculations
• Normal Depth: Uniform flow depth calculations
• Critical Depth: Critical flow depth analysis

#Aerodynamics and Forces

• Drag Force: Fluid resistance calculations (F_D = ½ρv²AC_D)
• Lift Force: Aerodynamic lift calculations (F_L = ½ρv²AC_L)
• Drag Coefficient: Flow resistance coefficients
• Lift Coefficient: Aerodynamic lift coefficients

#Dimensionless Numbers

• Weber Number: Surface tension effects (We = ρv²L/σ)
• Mach Number: Compressible flow analysis (Ma = v/a)
• Euler Number: Pressure difference analysis (Eu = Δp/ρv²)
• Dimensionless Analysis: Flow similarity and scaling

#Mathematical Utilities

• Power Functions: Square, cube, cube root calculations
• Logarithmic Functions: Base-10 logarithm approximations
• Trigonometric Functions: Advanced angle calculations
• Numerical Methods: Approximation and interpolation functions

#Usage

#Fluid Statics

test "hydrostatic pressure" {
  // Water depth 10m, water density 1000 kg/m³
  // p = p0 + ρgh = 101325 + 1000*9.80665*10 = 199391.5 Pa
  let p = hydrostatic_pressure_std(ATMOSPHERIC_PRESSURE, RHO_WATER, 10.0)
  assert_eq(approx_equal(p, 199391.5, 50.0), true)

  // Buoyant force
  let fb = buoyant_force_std(RHO_WATER, 1.0) // 1 m³ water
  assert_eq(approx_equal(fb, 9806.65, 1.0), true)
}

#Continuity Equation

test "continuity equation" {
  // Volume flow rate
  let q = volume_flow_rate(0.1, 2.0) // 0.1 m² * 2 m/s
  assert_eq(q, 0.2)

  // Velocity calculation from flow rate
  let v = velocity_from_flow_rate(0.2, 0.1)
  assert_eq(v, 2.0)

  // Mass flow rate
  let mdot = mass_flow_rate(RHO_WATER, 0.2)
  assert_eq(mdot, 200.0)
}

#Bernoulli Equation

test "bernoulli equation" {
  // Total head: z=5, p/(ρg)=10.19, v²/(2g)=0.459
  let h = bernoulli_total_head_std(5.0, 100000.0, RHO_WATER, 3.0)
  assert_eq(approx_equal(h, 15.65, 0.5), true)

  // Velocity head
  let hv = velocity_head(5.0, G)
  assert_eq(approx_equal(hv, 1.274, 0.01), true)
}

#Reynolds Number

test "reynolds number" {
  // Re = ρvD/μ
  // Water: ρ=1000, v=1 m/s, D=0.1 m, μ=0.001002
  // Re = 1000*1*0.1/0.001002 ≈ 99800
  let re = reynolds_number(RHO_WATER, 1.0, 0.1, MU_WATER_20C)
  assert_eq(approx_equal(re, 99800.0, 500.0), true)

  // Determine flow regime
  assert_eq(is_turbulent_pipe(5000.0), true)
  assert_eq(is_turbulent_pipe(1000.0), false)
}

#Laminar Flow

test "laminar flow" {
  // Laminar flow rate: Q = πΔpR⁴/(8μL)
  // Δp=1000 Pa, μ=0.001, L=10 m, R=0.05 m
  // Q = π*1000*0.05⁴/(8*0.001*10) = π*1000*0.00000625/0.08 = 0.245 m³/s
  let q = laminar_flow_rate(1000.0, MU_WATER_20C, 10.0, 0.05)
  assert_eq(approx_equal(q, 0.245, 0.01), true)

  // Laminar friction factor
  let f = laminar_friction_factor(1000.0)
  assert_eq(f, 0.064)
}

#Darcy-Weisbach Equation

test "darcy weisbach" {
  // Friction head loss
  // f=0.02, L=100 m, D=0.2 m, v=2 m/s
  // hf = 0.02*(100/0.2)*(4/(2*9.81)) = 0.02*500*0.204 = 2.04 m
  let hf = darcy_weisbach_head_loss_std(0.02, 100.0, 0.2, 2.0)
  assert_eq(approx_equal(hf, 2.04, 0.1), true)
}

#Local Losses

test "local losses" {
  // Local head loss
  let hl = local_head_loss_std(0.5, 3.0)
  assert_eq(approx_equal(hl, 0.229, 0.01), true)

  // Sudden expansion loss coefficient
  let k_exp = sudden_expansion_loss_coefficient(0.1, 0.2)
  assert_eq(approx_equal(k_exp, 0.25, 0.01), true)
}

#Manning Formula

test "manning formula" {
  // Rectangular open channel: b=2m, h=1m, n=0.013, S=0.001
  // A = 2*1 = 2 m², P = 2+2*1 = 4 m, R = 2/4 = 0.5 m
  // Q = (1/0.013)*2*0.5^(2/3)*0.001^(1/2)
  let r = hydraulic_radius_rect(2.0, 1.0)
  assert_eq(approx_equal(r, 0.5, 0.01), true)
  let q = manning_flow_rate(0.013, 2.0, 0.5, 0.001)
  assert_eq(q > 0.0, true)
}

#Froude Number

test "froude number" {
  // Fr = v/sqrt(gh)
  // v=2 m/s, h=1 m
  // Fr = 2/sqrt(9.81*1) = 0.639
  let fr = froude_number(2.0, G, 1.0)
  assert_eq(approx_equal(fr, 0.639, 0.01), true)

  // Flow regime classification
  assert_eq(flow_regime(0.5), "subcritical")
  assert_eq(flow_regime(1.0), "critical")
  assert_eq(flow_regime(2.0), "supercritical")
}

#Drag and Lift Forces

test "drag and lift" {
  // Drag force: F_D = 0.5*ρ*v²*A*C_D
  // ρ=1.204, v=10 m/s, A=1 m², C_D=0.5
  // F_D = 0.5*1.204*100*1*0.5 = 30.1 N
  let fd = drag_force(RHO_AIR, 10.0, 1.0, 0.5)
  assert_eq(approx_equal(fd, 30.1, 0.1), true)

  // Lift force: F_L = 0.5*ρ*v²*A*C_L = 0.5*1.204*100*1*0.8 = 48.16 N
  let fl = lift_force(RHO_AIR, 10.0, 1.0, 0.8)
  assert_eq(approx_equal(fl, 48.16, 0.1), true)
}

#Dimensionless Numbers

test "dimensionless numbers" {
  // Weber number
  let we = weber_number(RHO_WATER, 5.0, 0.1, SIGMA_WATER)
  assert_eq(we > 0.0, true)

  // Mach number
  let ma = mach_number(340.0, 340.0)
  assert_eq(ma, 1.0)

  // Euler number: Eu = Δp/(ρv²) = 1000/(1000*25) = 0.04
  let eu = euler_number(1000.0, RHO_WATER, 5.0)
  assert_eq(approx_equal(eu, 0.04, 0.01), true)
}

#Mathematical Tools

test "tools functions" {
  // Square and cube
  assert_eq(square(3.0), 9.0)
  assert_eq(cube(2.0), 8.0)

  // Cube root
  assert_eq(approx_equal(cbrt(27.0), 3.0, 0.0001), true)
  assert_eq(approx_equal(cbrt(8.0), 2.0, 0.0001), true)

  // Logarithm (approximate, with larger tolerance)
  assert_eq(approx_equal(log10_approx(100.0), 2.0, 0.3), true)
}

#Parameter Ranges

#Valid Input Ranges

• Pressure: 0–10⁸ Pa (fluid pressures)
• Density: 0.1–2000 kg/m³ (fluid densities)
• Viscosity: 10⁻⁶–10⁻² Pa·s (dynamic viscosities)
• Velocity: 0–100 m/s (flow velocities)
• Length/Diameter: 10⁻⁶–10² m (geometrical dimensions)
• Flow Rate: 10⁻⁹–10³ m³/s (volumetric flow rates)
• Reynolds Number: 1–10⁷ (flow regime classification)
• Froude Number: 0.1–10 (open channel flow)

#Typical Fluid Properties

• Water (20°C): ρ = 998.2 kg/m³, μ = 1.002×10⁻³ Pa·s
• Air (20°C): ρ = 1.204 kg/m³, μ = 1.81×10⁻⁵ Pa·s
• Standard Gravity: g = 9.80665 m/s²
• Atmospheric Pressure: p₀ = 101,325 Pa
• Water Surface Tension: σ = 0.0728 N/m
• Speed of Sound in Air: a = 343 m/s

#Testing

moon test

#Test Coverage

• Fluid statics (pressure, buoyancy, pressure centers)
• Continuity and Bernoulli equations
• Flow regime analysis (Reynolds, Froude numbers)
• Pipe flow calculations (laminar, turbulent, losses)
• Open channel flow (Manning equation, hydraulic radius)
• Aerodynamic forces (drag, lift coefficients)
• Dimensionless numbers and similarity
• Mathematical utility functions
• Boundary conditions and edge cases

#Technical Details

#Physical Principles

• Conservation Laws: Mass, energy, and momentum conservation
• Newtonian Fluids: Viscosity and shear stress relationships
• Pressure Fields: Hydrostatic and hydrodynamic pressure distributions
• Flow Similarity: Dimensional analysis and scaling laws
• Boundary Layers: Flow behavior near solid surfaces

#Mathematical Methods

• Algebraic Equations: Direct calculations for statics and simple flows
• Differential Equations: Energy and momentum balance equations
• Empirical Correlations: Friction factors and loss coefficients
• Numerical Approximations: Root finding and interpolation methods
• Statistical Analysis: Uncertainty and error propagation

#Engineering Standards

• SI Units: Consistent use of International System of Units
• Fluid Mechanics Conventions: Standard notation and terminology
• Engineering Accuracy: Appropriate precision for engineering calculations
• Safety Margins: Conservative design practices

#Computational Considerations

• Numerical Stability: Robust algorithms for wide parameter ranges
• Physical Limits: Validation of input parameters against physical bounds
• Unit Consistency: Automatic dimensional analysis
• Performance Optimization: Efficient calculations for engineering applications

#Notes

1. Units: All calculations use SI units (meters, kilograms, seconds, Pascals)
2. Fluid Properties: Default values provided for common fluids (water, air)
3. Flow Assumptions: Incompressible, Newtonian fluid assumptions unless specified
4. Temperature Effects: Standard conditions assumed unless temperature specified
5. Accuracy: Engineering precision suitable for design calculations
6. Boundary Conditions: Physical limits enforced to prevent unrealistic results
7. Convergence: Iterative methods include convergence checks
8. Validation: Results should be verified against experimental data or established correlations

#Application Scenarios

• Hydraulic Engineering: Pipeline design, pump selection, pressure vessel analysis
• Environmental Engineering: Water distribution systems, wastewater treatment
• Mechanical Engineering: Fluid machinery design, heat exchangers, ventilation systems
• Civil Engineering: Open channel flow, drainage systems, hydraulic structures
• Aerospace Engineering: Aerodynamic analysis, wind tunnel testing, aircraft design
• Chemical Engineering: Process piping, mixing systems, fluid transport
• Marine Engineering: Ship hydrodynamics, offshore structures, underwater systems
• Geotechnical Engineering: Groundwater flow, seepage analysis, dam design
• Energy Systems: Turbomachinery, renewable energy, power plant design
• Research Applications: Fluid dynamics research, computational fluid dynamics validation

#Version Information

• Fluid statics (pressure, buoyancy, surface forces)
• Flow analysis (continuity, Bernoulli, energy equations)
• Flow characteristics (Reynolds, Froude, Mach numbers)
• Pipe flow (laminar, turbulent, friction losses)
• Open channel flow (Manning equation, critical flow)
• Aerodynamic forces (drag, lift, coefficients)
• Dimensionless analysis (Weber, Euler numbers)
• Mathematical utilities (power functions, logarithms)