Calculate dimensionless numbers for fluid flow and other physical systems.
Dimensionless numbers are calculated from groups of variables so that the result is dimensionless. Dimensionless numbers can be calculated from any consistent set of units, and will have the same value. Dimensionless numbers can be a very powerful tool for analysing physical systems.
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CALCULATOR : Dimensionless Froude Number Fr From Wave Propagation Velocity (General Form) [FREE] ±
Calculate dimensionless Froude number Fr from wave propagation velocity (general form). The dimensionless Froude number is the ratio of inertia forces and gravity forces. It may be used to determine the resistance of a body moving through water, and also to determine the type of flow in open channels or shallow water waves. The Froude number was originally derived from the speed length ratio for ship resistance. Tool Input- V : Fluid Velocity
- c : Wave Celerity Or Propagation Speed
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CALCULATOR : Dimensionless Froude Number Fr For Ship Hydrodynamics [FREE] ±
Calculate dimensionless Froude number Fr for ship hydrodynamics. The dimensionless Froude number is the ratio of inertia forces and gravity forces. It may be used to determine the resistance of a body moving through water, and also to determine the type of flow in open channels or shallow water waves. The Froude number was originally derived from the speed length ratio for ship resistance. For ships the characteristic length is the waterline length. Tool Input- V : Fluid Velocity
- L : Water Line Length
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CALCULATOR : Dimensionless Froude Number Fr For Open Channels And Shallow Water Waves [FREE] ±
Calculate dimensionless Froude number Fr for open channels and shallow water waves. The dimensionless Froude number is the ratio of inertia forces and gravity forces. It may be used to determine the resistance of a body moving through water, and also to determine the type of flow in open channels or shallow water waves. The Froude number was originally derived from the speed length ratio for ship resistance. Tool Input- V : Fluid Velocity
- d : Channel Depth
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CALCULATOR : Dimensionless Weber Number We (General Form) [FREE] ±
Calculate dimensionless Weber number We. The dimensionless Weber number is the ratio of inertia forces and surface tension forces. It may be used to analyse thin film flows and the formation of droplets and bubbles during impact of an object onto a fluid surface. Tool Input- V : Fluid Velocity
- L : Characteristic Length
- ρ : Fluid Density
- σ : Surface Tension
Tool Output- We : Weber Number
- We* : Modified Weber Number
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CALCULATOR : Dimensionless Rayleigh Number Ra (General Form) [FREE] ±
Calculate dimensionless Rayleigh number Ra (general form). The dimensionless Rayleigh number is the ratio of buoyancy forces and viscous forces. The Rayleigh number is equal to the product of the Grashof number and the Prandtl number where the characteristic length equals the position (refer to Grashof number and Prandtl number). For ideal gases thermal expansion coefficient can be calculated from the gas temperature (either the surface temperature, bulk fluid temperature, or average temperature). Tool Input- visctype : Viscosity Type
- μu : User Defined Dynamic Viscosity
- νu : User Defined Kinematic Viscosity
- btype : Thermal Expansion Coefficient Type
- βu : User Defined Thermal Expansion Coefficient
- L : Characteristic Length
- Ts : Surface Temperature
- To : Fluid Temperature
- ρ : Fluid Density
- Cp : Fluid Heat Capacity Constant Pressure
- k : Fluid Heat Conductivity
Tool Output- α : Fluid Thermal Diffusivity
- β : Thermal Expansion Coefficient
- ν : Fluid Kinematic Viscosity
- Gr : Grashof Number
- Pr : Prandtl Number
- Ra : Rayleigh Number
- TΔ : Temperature Difference
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CALCULATOR : Dimensionless Strouhal Number St (General Form) [FREE] ±
Calculate dimensionless Strouhal number St (general form). The dimensionless Strouhal number is used to determine the onset and type of vortex shedding in oscillating flow. The Roshko number is equal to the product of the Strouhal number and the Reynolds number (refer to Roshko number and Reynolds number). Tool Input- L : Characteristic Length
- f : Vortex Shedding Frequency
- V : Fluid Velocity
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CALCULATOR : Dimensionless Grashof Number Gr (General Form) [FREE] ±
Calculate dimensionless Grashof number Gr (general form). The dimensionless Grashof number is the ratio of buoyancy forces and viscous forces acting on a heated fluid. The Grashof number may be used to determine the transition between laminar and turbulent boundary layer. The bulk fluid temperature should be used as the fluid temperature. The Rayleigh number is the product of the Grashof number and the Prandtl number (refer to Rayleigh number and Prandtl number). For ideal gases thermal expansion coefficient can be calculated from the gas temperature (either the surface temperature, bulk fluid temperature, or average temperature). Tool Input- visctype : Viscosity Type
- μu : User Defined Dynamic Viscosity
- νu : User Defined Kinematic Viscosity
- ρu : User Defined Density
- btype : Thermal Expansion Coefficient Type
- βu : User Defined Thermal Expansion Coefficient
- L : Characteristic Length
- Ts : Surface Temperature
- To : Fluid Temperature
Tool Output- β : Thermal Expansion Coefficient
- ν : Fluid Kinematic Viscosity
- Gr : Grashof Number
- TΔ : Temperature Difference
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CALCULATOR : Dimensionless Nusselt Number Nu (General Form) [FREE] ±
Calculate dimensionless Nusselt number Nu (general form). The dimensionless Nusselt number is the ratio of convective heat transfer and conductive heat transfer. For free convection the Nusselt number is often calculated from the Rayleigh number and the Prandtl number (refer to Rayleigh number and Prandtl number). For forced convection the Nusselt number is often calculated from the Reynolds number and the Prandtl number (refer to Reynolds number and Prandtl number). Tool Input- L : Characteristic Length
- h : Fluid Convective Heat Transfer
- k : Fluid Heat Conductivity
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CALCULATOR : Dimensionless Richardson Number Ri (Thermal Convection Form) [FREE] ±
Calculate dimensionless Richardson number Ri (thermal convection form). The dimensionless Richardson number is the ratio of buoyancy and flow shear, and can be used to determine the relative importance of natural convection and forced convection. Typically, natural convection is negligible when Ri < 0.1, and forced convection is negligible when Ri > 10. For ideal gases thermal expansion coefficient can be calculated from the gas temperature (either the surface temperature, bulk fluid temperature, or average temperature). Tool Input- btype : Thermal Expansion Coefficient Type
- βu : User Defined Thermal Expansion Coefficient
- L : Characteristic Length
- Ts : Surface Temperature
- To : Fluid Temperature
- V : Fluid Velocity
Tool Output- β : Thermal Expansion Coefficient
- Ri : Richardson Number
- TΔ : Temperature Difference
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CALCULATOR : Dimensionless Shields Number ϴ And Critical Fluid Velocity [FREE] ±
Calculate the dimensionless Shields number or Shields parameter ϴ and the critical fluid velocity for initiation of sediment movement. The Shields number is used to calculate the initiation of sediment movement in a fluid flow. For subsea waves and currents the critical Shields parameter is approximately 0.04. For laminar flow the critical Shields parameter is approximately 0.03. Tool Input- roughtype : Seabed Roughness Type
- D50u : User Defined Particle Diameter
- facttype : Critical Shields Parameter Type
- ϴcu : User Defined Critical Shields Number
- wavetype : Friction Factor Type
- Uc : Current Velocity
- Uw : Wave Horizontal Velocity
- T : Wave Period
- ρb : Seawater Density
- ρp : Particle Density
Tool Output- ϴ : Shields Parameter
- ϴcr : Critical Shields Parameter
- τ : Fluid Shear Stress
- CVG : Convergence Factor
- D50 : Mean Particle Diameter
- Ss : Particle Relative Density
- Ucr : Critical Fluid Velocity
- fw : Friction Factor
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CALCULATOR : Dimensionless Euler Number Eu From Fluid Velocity (General Case) [FREE] ±
Calculate dimensionless Euler number from fluid velocity (general case). The dimensionless Euler number is the ratio of fluid pressure loss to fluid kinetic energy. The Euler number is typically used to characterise friction loss through components. The flow diameter and elevation are assumed to be constant. The inlet and outlet pressure may be measured as either gauge pressure or absolute pressure provided that both pressures are measured in the same way. The equivalent K value equals 2 times the Euler number. Tool Input- V : Fluid Velocity
- ρ : Fluid Density
- Pi : Inlet Pressure
- Po : Outlet Pressure
Tool Output- Eu : Euler Number
- K : Equivalent K Factor
- PΔ : Delta Pressure
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CALCULATOR : Dimensionless Eckert Number Ec From Fluid Velocity (General Case) [FREE] ±
Calculate dimensionless Eckert number Ec from fluid velocity (general case). The dimensionless Eckert number is the ratio of the fluid kinetic energy to the fluid heat energy. For small Eckert numbers (Ec << 1), heat transfer is dominated by conduction and convection and kinetic effects may be ignored. The product of the Eckert number and the Prandtl number is equal to the Brinkman number (refer to Brinkman number). Tool Input- V : Fluid Velocity
- Cp : Specific Heat Capacity
- T1 : Fluid Temperature 1
- T2 : Fluid Temperature 2
Tool Output- ΔT : Temperature Difference
- Ec : Eckert Number
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CALCULATOR : Dimensionless Prandtl Number Pr (General Case) [FREE] ±
Calculate dimensionless Prandtl number Pr. The dimensionless Prandtl number is the ratio of the fluid viscosity to thermal diffusivity. The product of the Eckert number and the Prandtl number is equal to the Brinkman number (refer to Brinkman number and Eckert Number). The product of the Grashof number and the Prandtl number is equal to the Rayleigh number (refer to Rayleigh number and Grashof number). Tool Input- visctype : Viscosity Type
- μu : User Defined Dynamic Viscosity
- νu : User Defined Kinematic Viscosity
- ρ : Density
- Cp : Specific Heat Capacity Constant Pressure
- k : Fluid Heat Conductivity
Tool Output- α : Fluid Thermal Diffusivity
- ν : Fluid Kinematic Viscosity
- Pr : P Value
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CALCULATOR : Dimensionless Brinkman Number Br From Fluid Velocity (General Case) [FREE] ±
Calculate dimensionless Brinkman number Br from fluid velocity (general case). The dimensionless Brinkman number is the ratio of the fluid friction loss and the fluid thermal conduction. The Brinkman number is equal to the product of the Eckert number and the Prandtl number (refer to Eckert number and the Prandtl number). Tool Input- visctype : Viscosity Type
- μu : User Defined Dynamic Viscosity
- νu : User Defined Kinematic Viscosity
- V : Fluid Velocity
- ρ : Density
- Cp : Specific Heat Capacity Constant Pressure
- k : Fluid Heat Conductivity
- To : Fluid Temperature
- Ts : Surface Temperature
Tool Output- α : Fluid Thermal Diffusivity
- ν : Fluid Kinematic Viscosity
- Br : B Value
- Ec : E Value
- Pr : P Value
- TΔ : Temperature Difference
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CALCULATOR : Dimensionless Peclet Number Pe (Thermal Diffusion Case) [FREE] ±
Calculate dimensionless Peclet number Pe (thermal diffusion case). The dimensionless Peclet number is the ratio of advection and diffusion and is used in the analysis of fluid transport. For thermal diffusion the Peclet number is equal to the product of the Reynolds number and the Prandtl number (refer to Prandtl number and Reynolds number). Tool Input- visctype : Viscosity Type
- μu : User Defined Dynamic Viscosity
- νu : User Defined Kinematic Viscosity
- L : Characteristic Length
- V : Fluid Velocity
- ρ : Fluid Density
- Cp : Fluid Specific Heat
- k : Fluid Heat Conductivity
Tool Output- α : Fluid Thermal Diffusivity
- ν : Fluid Kinematic Viscosity
- Pe : Peclet Number
- Pr : Prandtl Number
- Re : Reynolds Number
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CALCULATOR : Dimensionless Peclet Number Pe (Mass Diffusion Case) [FREE] ±
Calculate dimensionless Peclet number Pe (mass diffusion case). The dimensionless Peclet number is the ratio of advection and diffusion and is used in the analysis of fluid transport. For mass diffusion the Peclet number is equal to the product of the Reynolds number and the Schmidt number (refer to Schmidt number and Reynolds number). Tool Input- visctype : Viscosity Type
- μu : User Defined Dynamic Viscosity
- νu : User Defined Kinematic Viscosity
- ρu : User Defined Density
- L : Characteristic Length
- V : Fluid Velocity
- D : Fluid Mass Diffusivity
Tool Output- ν : Fluid Kinematic Viscosity
- Pe : Peclet Number
- Re : Reynolds Number
- Sc : Schimdt Number
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CALCULATOR : Dimensionless Schmidt Number Sc [FREE] ±
Calculate dimensionless Schmidt number Sc. The dimensionless Schmidt number is the ratio of viscosity over mass diffusivity. The Peclet number is the mass diffusion equivalent of the Prandtl number for thermal diffusion (refer to Prandtl number). For mass diffusion the Peclet number is equal to product of the Reynolds number and the Schmidt number (refer to Peclet number and Reynolds number). Tool Input- visctype : Viscosity Type
- μu : User Defined Dynamic Viscosity
- νu : User Defined Kinematic Viscosity
- ρu : User Defined Density
- D : Fluid Mass Diffusivity
Tool Output- ν : Fluid Kinematic Viscosity
- Sc : Schimdt Number
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CALCULATOR : Dimensionless Roshko Number Ro (General Form) [FREE] ±
Calculate dimensionless Roshko number Ro (general form). The dimensionless Roshko number is equal to the product of the Reynolds number and the Strouhal number (refer to Strouhal number and Reynolds number). Tool Input- visctype : Viscosity Type
- μu : User Defined Dynamic Viscosity
- νu : User Defined Kinematic Viscosity
- ρu : User Defined Density
- L : Characteristic Length
- f : Frequency
Tool Output- ν : Fluid Kinematic Viscosity
- Ro : Roshko Number
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CALCULATOR : Dimensionless Sherwood Number Sh (General Form) [FREE] ±
Calculate dimensionless Sherwood number Sh (general form). The dimensionless Sherwood number is the ratio of convective mass transport and diffusive mass transport. The Sherwood number is the mass transfer equivalent of the Nusselt number (refer to Nusselt number). Tool Input- L : Characteristic Length
- D : Fluid Mass Diffusivity
- K : Fluid Heat Conductivity
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CALCULATOR : Dimensionless Number Liquid Density [FREE] ±
Calculate dimensionless number liquid density from specific gravity, degrees Baume, degrees Twaddell, or degrees API. For liquids lighter than or equal to water the density can be defined as degrees API, or degrees Baume (Be-). For liquids heavier than water the density can be defined by degrees Baume (Be+), or degrees Twaddell. Tool Input- sgtype : Density Type
- SGu : User Defined Specific Gravity
- Be+u : User Defined Degrees Baume SG > 1
- Be-u : User Defined Degrees Baume SG <= 1
- Twu : User Defined Degrees Twaddell SG > 1
- APIu : User Defined Degrees API SG <= 1
- ρu : User Defined Liquid Density
Tool Output- ρ : Fluid Density
- API : Degrees API SG ≤ 1
- Be+ : Degrees Baume SG > 1
- Be- : Degrees Baume SG ≤ 1
- SG : Specific Gravity
- Tw : Degrees Twaddell SG > 1
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CALCULATOR : Dimensionless Number Gas Density And Compressibility Factor [FREE] ±
Calculate dimensionless number gas density and compressibility factor from temperature, pressure and critical point constants. The compressibility factor can be calculated from either the Peng Robinson, Soave, Redlich Kwong, or van der Waals equation of state (EOS). The compressibility factor calculation is valid for gas phase only. Use the Result Plot option to plot compressibility factor versus pressure and temperature, compressibility factor versus pressure and equation of state type, or compressibility factor versus temperature and equation of state type. Tool Input- fluidtype : Fluid Type
- SGu : User Defined Gas Specific Gravity
- ωu : User Defined Acentric Factor
- Pcu : User Defined Critical Pressure
- Tcu : User Defined Critical Temperature
- eostype : Equation Of State
- Zu : User Defined Compressibility Factor
- P : Fluid Pressure
- T : Fluid Temperature
Tool Output- ρ : Fluid Density
- ω : Accentric Factor
- Pc : Critical Point Pressure
- Pr : Reduced Pressure
- SG : Gas Specific Gravity Relative To Air
- Tc : Critical Point Temperature
- Tr : Reduced Temperature
- Vm : Molar Volume
- Z : Compressibility Factor
- cvg : Convergence Check
- mw : Fluid Molar Mass
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CALCULATOR : Dimensionless Number Fresh Water Density From Temperature [FREE] ±
Calculate dimensionless number fresh water density from temperature at atmospheric pressure (IAPWS R7-97 steam table). The calculation is valid from the freezing point (0 C) to the boiling point (100 C). Use the Result Plot option to plot density versus temperature. Tool InputTool Output |
CALCULATOR : Dimensionless Number Salt Water Density From Temperature And Salinity [FREE] ±
Calculate dimensionless number salt water density at atmospheric pressure from temperature and salinity (TEOS-10). Practical salinity = parts per thousand of dissolved solids (mainly salt). The absolute salinity is taken as 35.16504 / 35 times the practical salinity. The absolute salinity anomaly δSA is ignored. Use the Result Plot option to plot density versus temperature. Tool InputTool Output |
CALCULATOR : Dimensionless Number Liquid Pipeline Density And Flowrate [FREE] ±
Calculate dimensionless number liquid pipeline flowrate. Liquid density can be defined by either specific gravity, degrees Baume, degrees Twaddell, or degrees API. For liquids lighter than or equal to water the density can be defined as degrees API, or degrees Baume (Be-). For liquids heavier than water the density can be defined by degrees Baume (Be+), or degrees Twaddell. Flowrate can be defined by volume flowrate, mass flowrate, or fluid velocity. Tool Input- schdtype : Pipe Schedule Type
- diamtype : Pipe Diameter Type
- ODu : User Defined Outside Diameter
- IDu : User Defined Inside Diameter
- wtntype : Wall Thickness Type
- tnu : User Defined Wall Thickness
- sgtype : Density Type
- SGu : User Defined Specific Gravity
- Be+u : User Defined Degrees Baume SG > 1
- Be-u : User Defined Degrees Baume SG <= 1
- Twu : User Defined Degrees Twaddell SG > 1
- APIu : User Defined Degrees API SG <= 1
- ρu : User Defined Liquid Density
- voltype : Fluid Flowrate Type
- Qfu : User Defined Volume Flow Rate
- Mfu : User Defined Mass Flow Rate
- Vfu : User Defined Fluid Velocity
Tool Output- ρ : Fluid Density
- API : Degrees API SG ≤ 1
- Be+ : Degrees Baume SG > 1
- Be- : Degrees Baume SG ≤ 1
- ID : Inside Diameter
- Mf : Liquid Mass Flowrate
- Qf : Liquid Volume Flowrate
- SG : Specific Gravity
- Tw : Degrees Twaddell SG > 1
- Vf : Fluid Velocity
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