Tools / Model test planner

Model test planner

A scale model can match the prototype’s Reynolds, Froude or Mach number, but usually only one of them. Enter the prototype and the model, and the planner shows the model speed each choice needs and how far the other two numbers are then off.

Prototype and model

Prototype speed, V_p (m/s) Prototype length, L_p (m) Model length, L_m (m) Gravity, g (m/s²)

Prototype fluid Density (kg/m³) Viscosity (µPa·s) Sound speed (m/s)

Model fluid Density (kg/m³) Viscosity (µPa·s) Sound speed (m/s)

0.2length scale, L_m/L_p6.16e+6prototype Re15.64prototype Fr0.1763prototype Mach

Match this	Model speed (m/s)	Re ratio	Fr ratio	Mach ratio	Model Mach	Force scale F_p/F_m
Reynolds number	20.62	1.000	0.7685	0.07892	0.01391	0.2598
Froude number	26.83	1.301	1.000	0.1027	0.01811	0.1534
Mach number	261.3	12.67	9.738	1.000	0.1763	0.001618

Ratios are model over prototype. Values far from 1 are shaded: that effect is not reproduced when you choose the row’s speed. A model Mach number above 0.3 means the model flow is itself compressible.

How to read it

Each row matches one number exactly (it shows 1.000 in its own column) and reports the model speed needed. The other columns give the model-to-prototype ratio of each number: a value of 1 means matched, and far from 1 means that effect is not reproduced in the model.

Reynolds number ρVL/μ matters for fully immersed bodies where viscous forces act, such as aircraft, vehicles and buildings.
Froude number V/√(gL) matters when gravity and a free surface act, such as ships, spillways and rivers.
Mach number V/c matters when compressibility matters, usually above Mach 0.3.

Force scale is F_p/F_m = ρ_pV_p²L_p² / (ρ_mV_m²L_m²), valid when the matched number is the one that governs the flow. Geometric similarity is assumed.