How Prandtl number is dependent on Pressure?

Raza Javed · August 13, 2019, 08:33

Hello Everyone,

I have a question related to the dependency of prandtl number on Pressure.

Air has a Prandtl number of 0.7 at atmospheric pressure.

If I want to lower the pressure of my fluid(air in my case) from atmospheric pressure then how can I find the new Prandtl number for this new pressure?

I know from the relation, that Prandtl number is not directly dependent on Pressure and it depends on thermal conductivity, specific heat and viscosity.

As I am changing the pressure, so I need to know how the Prandtl number will change?

Any help would be highly appreciated.

Thank you

geth03 · June 23, 2020, 09:52

of course the prandtl number is dependant of pressure.
for your fluid in interest you need to check how thermal conductivity, specific heat and viscosity change with regards to pressure and then figure it out
somehow.

https://www.researchgate.net/figure/...fig4_269800776

here you can see that thermal conductivity of water/steam increases with increasing pressure.

https://www.researchgate.net/figure/...fig2_269800776

here you can see that specific heat capacity of water/steam decreases with increasing pressure.

assuming a constant dynamic viscosity for example, because prandtl number is proportional to specific heat capacity to thermal conductivity ratio, an increase in pressure would mean a decrease in the prandtl number, assuming isothermal change, for the above shown water/steam.

August 13, 2019, 08:33	How Prandtl number is dependent on Pressure?	#1
Raza Javed Senior Member Raza Javed Join Date: Apr 2019 Location: Germany Posts: 183 Rep Power: 7	Hello Everyone, I have a question related to the dependency of prandtl number on Pressure. Air has a Prandtl number of 0.7 at atmospheric pressure. If I want to lower the pressure of my fluid(air in my case) from atmospheric pressure then how can I find the new Prandtl number for this new pressure? I know from the relation, that Prandtl number is not directly dependent on Pressure and it depends on thermal conductivity, specific heat and viscosity. As I am changing the pressure, so I need to know how the Prandtl number will change? Any help would be highly appreciated. Thank you

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June 23, 2020, 09:52		#2
geth03 Senior Member Join Date: Dec 2019 Location: Cologne, Germany Posts: 369 Rep Power: 8	of course the prandtl number is dependant of pressure. for your fluid in interest you need to check how thermal conductivity, specific heat and viscosity change with regards to pressure and then figure it out somehow. https://www.researchgate.net/figure/...fig4_269800776 here you can see that thermal conductivity of water/steam increases with increasing pressure. https://www.researchgate.net/figure/...fig2_269800776 here you can see that specific heat capacity of water/steam decreases with increasing pressure. assuming a constant dynamic viscosity for example, because prandtl number is proportional to specific heat capacity to thermal conductivity ratio, an increase in pressure would mean a decrease in the prandtl number, assuming isothermal change, for the above shown water/steam.