scaling

Convert quantities between model and prototype scale using Froude and Reynolds similitude.

Installation

pip install scaling

Usage

>>> from scaling import FroudeConverter
>>> froude = FroudeConverter()

>>> # Convert model value of 200 mm to prototype value (m) with scale of 10
>>> froude.model_to_proto(200, length_scale=10, input_unit='mm', target_unit='m')
2.0

>>> # Get Froude scaling exponent for quantities of time
>>> froude.scaling_exponent('s')
0.5

>>> # Get length, mass and time dimensions for quantities of energy
>>> froude.dimensions('kJ')
'L^2 M^1 T^-2'

Dataframes are also accepted, and specific units can be specified for the values in the index.

>>> T = 2
>>> H = 100

>>> # Generate regular waves with height=100mm, and period=2s
>>> t = np.arange(0, 10.1, 0.1)
>>> eta = 0.5 * H * np.sin(t * 2 * np.pi / T)

>>> df_model = pd.DataFrame(index=t, data=eta)
>>> df_model.columns = ['$\eta$ (mm)']
>>> df_model.index.name = 'Time (s)'

>>> df_model.plot()

>>> # Convert to prototype dimensions, with length scale=25
>>> df_proto = froude.model_to_proto(
        df_model,
        length_scale=25,
        input_unit='mm',
        target_unit='m',
        index_input_unit='s',
        index_target_unit='s')

>>> df_proto.columns = ['$\eta$ (m)']
>>> df_proto.plot()

scaling uses pint for unit and dimension conversions. pint is able to interpret a wide range of different input units.

>>> # Convert water head model value (mm) to prototype pressure value (kPa)
>>> froude.model_to_proto(10, length_scale=100, 'mm.H20', 'kPa')
9.80665

>>> # Demonstrate different ways of specifying units of newtons
>>> froude.dimensions('N')
'L^1 M^1 T^-2'
>>> froude.dimensions('newton')
'L^1 M^1 T^-2'
>>> froude.dimensions('kg.m/s/s')
'L^1 M^1 T^-2'
>>> froude.dimensions('kilogram.metre/second^2')
'L^1 M^1 T^-2'

Froude scaling reference

Quantity	Dimensions	Scaling exponent
Length	L^1	λ^1
Mass	M^1	λ^3
Time	T^1	λ^0.5
Velocity	L^1 T^-1	λ^0.5
Acceleration	L^1 T^-2	λ^0
Force	L^1 M^1 T^-2	λ^3
Pressure	L^-1 M^1 T^-2	λ^1
Overtopping	L^2 T^-1	λ^1.5

Reynolds scaling reference

Quantity	Dimensions	Scaling exponent
Length	L^1	λ^1
Mass	M^1	λ^3
Time	T^1	λ^2
Velocity	L^1 T^-1	λ^-1
Acceleration	L^1 T^-2	λ^-3
Force	L^1 M^1 T^-2	λ^0
Pressure	L^-1 M^1 T^-2	λ^-2
Overtopping	L^2 T^-1	λ^0