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Catégorie :Category: nCreator TI-Nspire
Auteur Author: djksfksdlajf
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 3.80 Ko KB
Mis en ligne Uploaded: 06/03/2025 - 09:26:06
Uploadeur Uploader: djksfksdlajf (Profil)
Téléchargements Downloads: 3
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4526498
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 3.80 Ko KB
Mis en ligne Uploaded: 06/03/2025 - 09:26:06
Uploadeur Uploader: djksfksdlajf (Profil)
Téléchargements Downloads: 3
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4526498
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
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Complete List of Equations with Variable Definitions 1. Hillslope Diffusion Equation Q s = D d Z d x Q_s = -D frac{dZ}{dx} Where: Q s Q_s = Sediment flux (rate of sediment movement per unit width per time) D D = Diffusivity coefficient (determines how easily sediment moves) d Z d x frac{dZ}{dx} = Slope gradient (rate of elevation change along the slope) This equation describes diffusive sediment transport , where more sediment moves as the slope increases. 2. Steady-State Hillslope Evolution U = D d 2 Z d x 2 U = D frac{d^2Z}{dx^2} Where: U U = Uplift rate (rate at which land surface rises) D D = Diffusivity coefficient (rate of sediment movement due to slow processes) d 2 Z d x 2 frac{d^2Z}{dx^2} = Hillslope curvature (rate of change of slope) This equation applies when uplift and erosion rates are balanced , keeping the hillslope stable over time. 3. Nonlinear Sediment Flux Equation Q s = D S + k ( S S c ) n Q_s = D S + k (S - S_c)^n Where: Q s Q_s = Sediment flux (rate of sediment movement) D D = Diffusivity coefficient (controls sediment transport in low slopes) S S = Slope gradient (steepness of the slope) k k = Transport coefficient for steep slopes S c S_c = Critical slope (threshold where landslides begin) n n = Empirical exponent (typically around 2) This equation accounts for both diffusive and landslide-driven transport , showing that sediment flux increases rapidly when the slope reaches a threshold. 4. Shear Stress Equation (Fluid Flow Over a Surface) Ä = Á g h S tau = rho g h S Where: Ä tau = Shear stress (force per unit area acting parallel to the surface) (Pa) Á rho = Density of water (kg/m³) g g = Gravitational acceleration (9.81 m/s²) h h = Flow depth (m) S S = Slope gradient (unitless) This equation determines how much force water exerts on the riverbed , controlling sediment transport and erosion. 5. Rational Method for Runoff Q = C I A Q = C I A Where: Q Q = Peak runoff discharge (m³/s) C C = Runoff coefficient (depends on land cover and soil properties) I I = Rainfall intensity (mm/hr) A A = Drainage area (km²) This equation estimates peak storm runoff from a watershed based on rainfall intensity and land characteristics. 6. Mannings Equation for River Flow V = 1 n R h 2 / 3 S 1 / 2 V = frac{1}{n} R_h^{2/3} S^{1/2} Where: V V = Depth-averaged velocity of flow (m/s) n n = Mannings roughness coefficient (depends on riverbed texture) R h R_h = Hydraulic radius (cross-sectional area of flow divided by wetted perimeter) S S = Channel bed slope (m/m) This equation estimates flow velocity in rivers based on channel roughness and slope. 7. Discharge Equation for Rivers Q = V A Q = V A Where: Q Q = Discharge (volume of water flowing through a section per unit time) (m³/s) V V = Flow velocity (m/s) A A = Cross-sectional area of the river (m²) This equation calculates how much water passes through a river section at a given time. 8. Drainage Density Equation D D = L A DD = frac{L}{A} Where: D D DD = Drainage density (km/km²) L L = Total length of streams and rivers in a watershed (km) A A = Total area of the watershed (km²) This equation measures how well a landscape is drained by streams , with higher values indicating more channels per area. 9. Sediment Detachment by Shear Stress D = k Ä n D = k tau^n Where: D D = Sediment detachment rate (kg/m²/s) k k = Erodibility coefficient (depends on soil type) Ä tau = Shear stress from water flow (Pa) n n = Empirical exponent (depends on sediment properties) This equation describes how sediment is detached from the land surface when the shear stress exceeds a critical value. 10. Cosmogenic Surface Exposure Dating N = P e » t N = P e^{-lambda t} Where: N N = Nuclide concentration in rock or sediment P P = Production rate of cosmogenic isotopes (e.g., 10Be, 26Al) » lambda = Decay constant of the isotope (1/time) t t = Time since surface exposure (years) This equation is used to estimate how long a rock has been exposed at the Earths surface , helping determine erosion rates and landscape evolution. 11. Catchment-Averaged Erosion Rate E = P N E = frac{P}{N} Where: E E = Erosion rate (mm/yr) P P = Cosmogenic isotope production rate (atoms/g/yr) N N = Measured nuclide concentration (atoms/g) This equation helps determine how fast a landscape is eroding over time using isotope measurements in stream sediment. Made with nCreator - tiplanet.org
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Compatible OS 3.0 et ultérieurs.
<<
Complete List of Equations with Variable Definitions 1. Hillslope Diffusion Equation Q s = D d Z d x Q_s = -D frac{dZ}{dx} Where: Q s Q_s = Sediment flux (rate of sediment movement per unit width per time) D D = Diffusivity coefficient (determines how easily sediment moves) d Z d x frac{dZ}{dx} = Slope gradient (rate of elevation change along the slope) This equation describes diffusive sediment transport , where more sediment moves as the slope increases. 2. Steady-State Hillslope Evolution U = D d 2 Z d x 2 U = D frac{d^2Z}{dx^2} Where: U U = Uplift rate (rate at which land surface rises) D D = Diffusivity coefficient (rate of sediment movement due to slow processes) d 2 Z d x 2 frac{d^2Z}{dx^2} = Hillslope curvature (rate of change of slope) This equation applies when uplift and erosion rates are balanced , keeping the hillslope stable over time. 3. Nonlinear Sediment Flux Equation Q s = D S + k ( S S c ) n Q_s = D S + k (S - S_c)^n Where: Q s Q_s = Sediment flux (rate of sediment movement) D D = Diffusivity coefficient (controls sediment transport in low slopes) S S = Slope gradient (steepness of the slope) k k = Transport coefficient for steep slopes S c S_c = Critical slope (threshold where landslides begin) n n = Empirical exponent (typically around 2) This equation accounts for both diffusive and landslide-driven transport , showing that sediment flux increases rapidly when the slope reaches a threshold. 4. Shear Stress Equation (Fluid Flow Over a Surface) Ä = Á g h S tau = rho g h S Where: Ä tau = Shear stress (force per unit area acting parallel to the surface) (Pa) Á rho = Density of water (kg/m³) g g = Gravitational acceleration (9.81 m/s²) h h = Flow depth (m) S S = Slope gradient (unitless) This equation determines how much force water exerts on the riverbed , controlling sediment transport and erosion. 5. Rational Method for Runoff Q = C I A Q = C I A Where: Q Q = Peak runoff discharge (m³/s) C C = Runoff coefficient (depends on land cover and soil properties) I I = Rainfall intensity (mm/hr) A A = Drainage area (km²) This equation estimates peak storm runoff from a watershed based on rainfall intensity and land characteristics. 6. Mannings Equation for River Flow V = 1 n R h 2 / 3 S 1 / 2 V = frac{1}{n} R_h^{2/3} S^{1/2} Where: V V = Depth-averaged velocity of flow (m/s) n n = Mannings roughness coefficient (depends on riverbed texture) R h R_h = Hydraulic radius (cross-sectional area of flow divided by wetted perimeter) S S = Channel bed slope (m/m) This equation estimates flow velocity in rivers based on channel roughness and slope. 7. Discharge Equation for Rivers Q = V A Q = V A Where: Q Q = Discharge (volume of water flowing through a section per unit time) (m³/s) V V = Flow velocity (m/s) A A = Cross-sectional area of the river (m²) This equation calculates how much water passes through a river section at a given time. 8. Drainage Density Equation D D = L A DD = frac{L}{A} Where: D D DD = Drainage density (km/km²) L L = Total length of streams and rivers in a watershed (km) A A = Total area of the watershed (km²) This equation measures how well a landscape is drained by streams , with higher values indicating more channels per area. 9. Sediment Detachment by Shear Stress D = k Ä n D = k tau^n Where: D D = Sediment detachment rate (kg/m²/s) k k = Erodibility coefficient (depends on soil type) Ä tau = Shear stress from water flow (Pa) n n = Empirical exponent (depends on sediment properties) This equation describes how sediment is detached from the land surface when the shear stress exceeds a critical value. 10. Cosmogenic Surface Exposure Dating N = P e » t N = P e^{-lambda t} Where: N N = Nuclide concentration in rock or sediment P P = Production rate of cosmogenic isotopes (e.g., 10Be, 26Al) » lambda = Decay constant of the isotope (1/time) t t = Time since surface exposure (years) This equation is used to estimate how long a rock has been exposed at the Earths surface , helping determine erosion rates and landscape evolution. 11. Catchment-Averaged Erosion Rate E = P N E = frac{P}{N} Where: E E = Erosion rate (mm/yr) P P = Cosmogenic isotope production rate (atoms/g/yr) N N = Measured nuclide concentration (atoms/g) This equation helps determine how fast a landscape is eroding over time using isotope measurements in stream sediment. Made with nCreator - tiplanet.org
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