Dynamic Viscosity#

The equation from Sengers and Watson was used to make a simplified equation

\[μ_s = \frac {10^5}{a + b\cdot T + c\cdot T^2 + d\cdot T^3} \tag{9}\]

where

Var

Description

μs

is the dynamic viscosity liquid water, kg/m s

T

is temperature of the water °C

a

is 557.82468

b

is 19.408782

c

is 0.1360459

d

is -3.1160832e-04

The units for the y axis kg/(m s) have been corrected so that the plot displays between 800 to 1800 between 0 and 30°C. The basis for this was that the uncorrected formula plotted between 0.00080 and 0.00180 and the viscosity of water at 20°C and 1 bar is \(1002.0\cdot 10^{-06}kg/m s\), shown at the end of the dynamic viscosity section in the paper by Popiel and Wojtkowiak (probably a misprint in my copy).

Hint

Hover your mouse over the intersection between the plot and 20°C, the tooltip shows 1002.1.

Show/Hide Code 09dyn_viscy.py 
import altair as alt
import numpy as np
import pandas as pd

T = np.linspace(0, 30, 31)

ms = 1e06 / (557.82468 + 19.408782 * T + 0.1360459 * np.power(T, 2) - \
    3.1160832e-04 * np.power(T, 3))

source = pd.DataFrame({
  'Temperature °C': T,
  'Dynamic Viscosity': ms
})

chart = alt.Chart(source).mark_line().encode(
    x=alt.X('Temperature °C', axis=alt.Axis(title='Temperature °C')),
    y=alt.Y('Dynamic Viscosity', axis=alt.Axis(title='Dynamic Viscosity  x 1e-06 kg/(m s)'),
           scale=alt.Scale(domain=(800, 1800))
           ),
    tooltip=['Temperature °C', alt.Tooltip('Dynamic Viscosity', format='.1f')]
).properties(
        title={
            "text": "Dynamic Viscosity of Saturated Liquid Water",
            "color": "#282828"
        }
    )

chart.save('dyn_viscy.html')

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