How to use the Fluid Dynamics Calculator
Choose a mode, enter positive values with a unit for each field, and select Calculate. Calculation values are processed in your browser. The result can include statistics, warnings, and Formula & steps.
Calculate Reynolds number
- Select Reynolds Number.
- Enter all four required values: Fluid density (ρ), Dynamic viscosity (μ), Pipe diameter (D), and Flow velocity (V). Select the unit for each value.
- Select Calculate to see the Reynolds number and flow classification.
Calculate pressure drop
- Select Pressure Drop.
- Enter Dynamic viscosity (μ), Pipe length (L), Pipe diameter (D), Flow velocity (V), and Fluid density (ρ). Select the unit for each field.
- Select Calculate to review pressure drop, Reynolds number, warnings, and Formula & steps.
Use Flow Velocity / Flow Rate controls
- Select Flow Velocity / Flow Rate, then select Velocity to calculate velocity from flow rate and area, or select Flow rate to calculate flow rate from velocity and area.
- Enter Cross-sectional area (A), or select Compute area from diameter (circular pipe: A = π D² / 4) and enter the pipe diameter. With the checkbox selected, the diameter-based circular-pipe area replaces the manually entered area.
- Enter the displayed flow rate or velocity value, select its unit, and then select Calculate.
Run, review, and reset a calculation
- Select Calculate to display statistics, warnings, and Formula & steps.
- Use Copy result or Download result (.txt) to save the plain-text result. A pressure-drop download includes Pa, psi, and an atm value.
- Select Reset to clear the inputs and result. If you change the calculation mode or the Velocity/Flow rate option, the existing result is hidden. Select Calculate again to create a new result.
The Governing Formulas
Reynolds number (ratio of inertial to viscous forces):
Re = ρ V D / μ
Flow rate and velocity through a cross-section, assuming a uniform bulk velocity profile:
Q = V × AV = Q / A
For a circular pipe, area can be computed directly from diameter: A = π D² / 4.
Pressure drop for steady, fully-developed laminar flow of an incompressible Newtonian fluid in a straight circular pipe (Hagen-Poiseuille equation):
ΔP = 32 μ L V / D²
where ρ is fluid density, V is average flow velocity, D is pipe diameter, μ is dynamic viscosity, A is cross-sectional area, L is pipe length, and ΔP is pressure drop along the pipe length.
What the results mean
The calculator classifies flow in a straight circular pipe as laminar when Re < 2300, transitional from 2300 to 4000, and turbulent when Re > 4000. These are conventional approximations; actual transition also depends on roughness, entrance effects, and disturbances. Pressure-drop results include a warning when the calculated Reynolds number is not laminar.
Units, validation, and controls
- Density: kg/m³, g/cm³, or lb/ft³.
- Dynamic viscosity: Pa·s, cP (centipoise), or lb/(ft·s).
- Pipe diameter / length: meters, centimeters, millimeters, inches, or feet.
- Cross-sectional area: m², cm², mm², in², or ft² - or computed automatically from diameter for a circular pipe.
- Velocity: m/s, ft/s, cm/s, or km/h.
- Flow rate: m³/s, L/s, L/min, gal/min (US), or ft³/s.
Supported units convert internally to consistent SI units before calculation, so different unit systems can be used for different fields.
Fields must contain numbers greater than zero. Empty, zero, negative, non-numeric, and comma-separated entries are rejected; the numeric parser also does not accept scientific notation. Inputs greater than 1e15 are rejected, and non-finite calculated results are rejected.
Assumptions and model limitations
The pressure-drop mode applies the Hagen-Poiseuille equation to steady, fully developed laminar flow of an incompressible Newtonian fluid in a straight circular pipe. It does not model fittings, bends, valves, entrance or exit losses, pipe roughness, or turbulent friction factors. The calculator does not design piping systems, select pumps or pipe sizes, or replace engineering advice.
Privacy and processing
Calculation values are processed locally by the calculator script. The page also loads analytics, and its subscription form sends submitted email addresses to /assets/subscribe.php.
Frequently Asked Questions
What is the Reynolds number formula?
The Reynolds number is Re = ρ V D / μ, where ρ is fluid density, V is flow velocity, D is pipe diameter, and μ is dynamic viscosity. It is a dimensionless ratio of inertial to viscous forces used to predict whether flow is laminar or turbulent.
What Reynolds number thresholds does this calculator use?
For flow in a straight circular pipe, this calculator classifies Re below 2300 as laminar, Re between 2300 and 4000 as transitional, and Re above 4000 as turbulent. These are the conventional textbook thresholds, not an exact physical boundary - real transition depends on pipe roughness, disturbances, and entrance conditions.
How is pressure drop calculated?
This calculator uses the Hagen-Poiseuille equation, ΔP = 32 μ L V / D², which applies only to steady, fully-developed laminar flow of an incompressible Newtonian fluid in a straight circular pipe. If the computed Reynolds number for your inputs is not laminar, the calculator shows an explicit warning that the result is not valid for those conditions.
Can this calculator design a piping system?
No. This tool performs deterministic arithmetic using documented, simplified fluid-dynamics formulas. It does not size pipes or select pumps, and its output is not certified engineering advice.
Can I compute the cross-sectional area from a pipe diameter?
Yes. In Flow Velocity / Flow Rate mode, select Compute area from diameter (circular pipe: A = π D² / 4) instead of entering the area manually.