This is a dimentionless number because the units of the numerator are canceled out by the units of the denominator thus making the units [-] or dimentionless ergo there is no physical meaning behind the number. Ex.: 2 [m/s] means that 2m is covered every second. You can measure a second and you can measure two meteres. In this case however, the momentum difusivity (which can be measure) is in stead rationalized relative to the thermal diffusivity (which can also be measured) however, the resultant ratio is a magnifigcation factor, not a physical factor. This means that if Pr=1, the momentum diffusivity is equal to the thermal diffusivity then the the relative ratio is (1:1) however, this does not manifaest in a direct, measureable way. If Pr=2 then we see that the momentum diffusivity is twice the thermal dffusivity, then we know that the ratio is (2:1) however, we can't disern simply from the number wether there was T temperature increase from this or M momentum loss.
I appreciate the comparison of velocity and temperature profile in the sketch of the flow.
Thank you for your channel ....you helped me pass a numerical computation unit with your numerical analysis Playlist...Quality content🇰🇪
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What makes the number dimensionless
This is a dimentionless number because the units of the numerator are canceled out by the units of the denominator thus making the units [-] or dimentionless ergo there is no physical meaning behind the number. Ex.: 2 [m/s] means that 2m is covered every second. You can measure a second and you can measure two meteres. In this case however, the momentum difusivity (which can be measure) is in stead rationalized relative to the thermal diffusivity (which can also be measured) however, the resultant ratio is a magnifigcation factor, not a physical factor. This means that if Pr=1, the momentum diffusivity is equal to the thermal diffusivity then the the relative ratio is (1:1) however, this does not manifaest in a direct, measureable way. If Pr=2 then we see that the momentum diffusivity is twice the thermal dffusivity, then we know that the ratio is (2:1) however, we can't disern simply from the number wether there was T temperature increase from this or M momentum loss.