Basic Fluid mechanics

mouli1991 · May 8, 2013, 04:51

Hello everyone
I have very bad knowldege in fluid mechanics..Explain me about Newtanion fluid.I need the derivation for the topic called "CONSTITUTIVE EQUATIONS FOR NEWTONION FLUID"(or viscous fluid)..some 6 equations like
towxx=2M(mu)(du/dx)
similar for yy and zz
include xy,yz and zx..
explain me pls

Rami · May 29, 2013, 06:01

Hi Sayee Chandrasekara Mouli,

Newtonian fluid means there is a linear relation between the stress and the strain-rate tensors (analogous to elasticity, where the stress is proportional to the strain). This is written (in tensor notation) as
Sik = -p * Iik +lambda * Emm * Iik + 2*mu * Eik
where Sik is the stress, Eik is the strain-rate, p is the pressure, Iik is the identity tensor, mu is the viscosity, muv is the bulk viscosity (usually assumed 0, i.e., Stokesw assumption) and lambda=muv - 2/3* mu is similar to Lame constant in elasticity.

The viscous stress, Tik, is defined as
Tik = Sik + p * Iik

The stain-rate is related to the velocity vector Ui through
2*Eik = Ui,k + Uk,i

From these relations you can easily derive the relations you asked about.

Rami

May 8, 2013, 04:51	Basic Fluid mechanics	#1
mouli1991 New Member Sayee chandrasekara mouli Join Date: Mar 2012 Posts: 21 Rep Power: 14	Hello everyone I have very bad knowldege in fluid mechanics..Explain me about Newtanion fluid.I need the derivation for the topic called "CONSTITUTIVE EQUATIONS FOR NEWTONION FLUID"(or viscous fluid)..some 6 equations like towxx=2M(mu)(du/dx) similar for yy and zz include xy,yz and zx.. explain me pls

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May 29, 2013, 06:01		#2
Rami Senior Member Rami Ben-Zvi Join Date: Mar 2009 Posts: 155 Rep Power: 17	Hi Sayee Chandrasekara Mouli, Newtonian fluid means there is a linear relation between the stress and the strain-rate tensors (analogous to elasticity, where the stress is proportional to the strain). This is written (in tensor notation) as Sik = -p * Iik +lambda * Emm * Iik + 2mu Eik where Sik is the stress, Eik is the strain-rate, p is the pressure, Iik is the identity tensor, mu is the viscosity, muv is the bulk viscosity (usually assumed 0, i.e., Stokesw assumption) and lambda=muv - 2/3* mu is similar to Lame constant in elasticity. The viscous stress, Tik, is defined as Tik = Sik + p * Iik The stain-rate is related to the velocity vector Ui through 2*Eik = Ui,k + Uk,i From these relations you can easily derive the relations you asked about. Rami