Reynolds number, inertial force, viscous force

lookat2309 · January 17, 2018, 17:14

Dear all:
I have a question regarding the Reynolds number. Reynolds number is the ratio of inertial forces to viscous forces.
Here is the content of the Website "https://www.grc.nasa.gov/www/BGH/reynolds.html".
"From a detailed analysis of the momentum conservation equation, the inertial forces are characterized by the product of the density r times the velocity V times the gradient of the velocity dV/dx. The viscous forces are characterized by the dynamic viscosity coefficient mu times the second gradient of the velocity d^2V/dx^2."

How can I derive the viscous forces: "d^2V/dx^2"?
Thanks .

Dave Kang

FMDenaro · January 17, 2018, 17:31

The viscous term in the momentum equation is due to the action of the deviatoric part of the stress tensor, that is div tau, and if the newtonian model is introduced you write tau = 2 mugrad v.Only for the incompressible model you can expand
div (2 mu grad v) = mu Lap v

lookat2309 · January 18, 2018, 05:02

Hi, thanks for your reply. I am still confused and trying my best to derive the equation. Was it possible for you to email me more detail information when you were free?
Email: yuchi.kang@bth.se

FMDenaro · January 18, 2018, 05:16

Quote:

Originally Posted by lookat2309

Hi, thanks for your reply. I am still confused and trying my best to derive the equation. Was it possible for you to email me more detail information when you were free?
Email: yuchi.kang@bth.se

There is nothing hidden in that, you can find all the details in any good fluid dynamics textbook. For example, have a read to the book of Kundu.

lookat2309 · January 18, 2018, 11:07

Thanks. Finally, I understand the whole.

January 17, 2018, 17:14	Reynolds number, inertial force, viscous force	#1
lookat2309 New Member Yuchi Kang Join Date: Feb 2017 Posts: 3 Rep Power: 9	Dear all: I have a question regarding the Reynolds number. Reynolds number is the ratio of inertial forces to viscous forces. Here is the content of the Website "https://www.grc.nasa.gov/www/BGH/reynolds.html". "From a detailed analysis of the momentum conservation equation, the inertial forces are characterized by the product of the density r times the velocity V times the gradient of the velocity dV/dx. The viscous forces are characterized by the dynamic viscosity coefficient mu times the second gradient of the velocity d^2V/dx^2." How can I derive the viscous forces: "d^2V/dx^2"? Thanks . Dave Kang

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January 17, 2018, 17:31		#2
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,882 Rep Power: 73	The viscous term in the momentum equation is due to the action of the deviatoric part of the stress tensor, that is div tau, and if the newtonian model is introduced you write tau = 2 mugrad v.Only for the incompressible model you can expand div (2 mu grad v) = mu Lap v

January 18, 2018, 05:02		#3
lookat2309 New Member Yuchi Kang Join Date: Feb 2017 Posts: 3 Rep Power: 9	Hi, thanks for your reply. I am still confused and trying my best to derive the equation. Was it possible for you to email me more detail information when you were free? Email: yuchi.kang@bth.se

January 18, 2018, 11:07		#5
lookat2309 New Member Yuchi Kang Join Date: Feb 2017 Posts: 3 Rep Power: 9	Thanks. Finally, I understand the whole.