# 4 Equations and 13 Unknowns

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• Posts: 84Member
edited January 29

Hi Karthik,

In one of the basic turbulent flow video the instructor is saying that in Incompressible Navier stroke equation we have 4 equations and 4unknowns(u,v,w,p) which is correct but the instructor is saying that after averaging we are getting 13 unknowns how? We are getting only three additional unknowns so, total it becomes 7unknowns not 13 right? And the additional unknowns which we are getting after averaging is nothing but the fluctuations of velocity in each direction.

Can you please help me on this? For your reference I have attached the SS where the instructor is saying that we have 13 unknowns after averaging.

Thank you,

Abubakar khan

• Posts: 243Member

Hello Abubakar,

For RANS equations, the unknowns are not the velocity fluctuations, they are infact the product of velocity fluctuations. Therefore, the total unknowns are u,v,w,p,u'u',u'v',u'w',v'u',v'v',v'w',w'u',w'v',w'w' = 13. Making use of the symmetric nature of the stress tensor, we can safely say u'v'=v'u', u'w'=w'u', v'w'=w'v'. Therefore, the actual number of unknowns are 10!

Regards,

Kalyan

PS - I dropped the bar from the terms for simplicity.

• Posts: 84Member
edited January 30

Hi Kalyan Sir,

I got my answer, thanks for clearing my doubt.

I have a request, can you please make a video on a SIMPLE and PISO algorithm.

@Kalyan Goparaju

Thank you,

Abubakar khan

• Posts: 84Member

Hi Kalyan Sir,

I got my answer, thanks for clearing my doubt. I have a request, can you please make a video on SIMPLE and PISO algorithm.

@Kalyan GoparajuThank you,

Abubakar khan