# Transport Phenomena Fluid Dynamics

Content type
User Generated
Subject
Chemical Engineering
School
New Mexico State University
Type
Homework
Rating
Showing Page:
1/9
1. For each of the following velocity distributions for a Newtonian fluid, draw a meaningful
sketch showing flow pattern. Also, evaluate (i) , (ii)  , (iii) , (iv)
, (v)
, (vi)
, and
(vii) for each case.
Newton’s Law of Viscosity:


  





 
  
 
Divergence of the velocity vector
 



Curl of vector fields:
 






For convective momentum transport:


a)


Divergence of the velocity vector:
 





Viscous stress tensor components:

Showing Page:
2/9






































x-direction convective momentum transport:









y-direction convective momentum transport:










z-direction convective momentum transport:




Showing Page:
3/9

End of Preview - Want to read all 9 pages?
Access Now
Unformatted Attachment Preview
1. For each of the following velocity distributions for a Newtonian fluid, draw a meaningful sketch showing flow pattern. Also, evaluate (i) 𝛻. 𝑣¯, (ii) 𝛻 × 𝑣¯, (iii) 𝛻𝑣¯, (iv) 𝜏¯ , (v) 𝛥¯, (vi) 𝜔¯ , and (vii) 𝜌𝑣¯𝑣¯for each case. Newton’s Law of Viscosity: 𝜕𝑣𝑗 𝜕𝑣𝑦 𝜕𝑣𝑖 2 𝜕𝑣𝑥 𝜕𝑣𝑧 𝜏𝑖𝑗 = −𝜇 ( + ) + ( 𝜇 − 𝜅) ( + + )𝛿 𝜕𝑥𝑖 𝜕𝑥𝑗 3 𝜕𝑥 𝜕𝑦 𝜕𝑧 𝑖𝑗 2 𝜏 = −𝜇(𝛻𝑣¯ + (𝛻𝑣¯)𝑡 ) + ( 𝜇 − 𝜅) (𝛻 ⋅ 𝑣¯)𝛿 3 Divergence of the velocity vector 𝜕𝑣𝑦 𝜕𝑣𝑥 𝜕𝑣𝑧 (𝛻 ⋅ 𝑣¯) = ( + + ) 𝜕𝑥 𝜕𝑦 𝜕𝑧 Curl of vector fields: 𝜕𝑣𝑦 𝜕𝑣𝑦 𝜕𝑣𝑧 𝜕𝑣𝑥 𝜕𝑣𝑧 𝜕𝑣𝑥 ) 𝛿𝑦 + ( 𝛻×𝑣 = ( − ) 𝛿𝑥 + ( − − )𝛿 𝜕𝑦 𝜕𝑧 𝜕𝑧 𝜕𝑥 𝜕𝑥 𝜕𝑦 𝑧 For convective momentum transport: 𝜌𝑣𝑖 𝑣𝑗 = 𝛴𝑖 𝛴𝑗 𝛿𝑖 𝛿𝑗 𝜌𝑣𝑖 𝑣𝑗 a) 𝑣𝑥 = 1 2 𝑦 𝑣𝑦 = 0 𝑣𝑧 = 0 Divergence of the velocity vector: 1 𝜕 (2 𝑦) 𝜕(0) 𝜕(0) (𝛻 ⋅ 𝑣¯) = ( ) = 0 + + 𝜕𝑥 𝜕𝑦 𝜕𝑧 Viscous stress tensor components: 𝜏𝑥𝑥 1 𝜕 (2 𝑦) 𝜕𝑣𝑥 = −2𝜇 = −2𝜇 = 0 𝜕𝑥 𝜕𝑥 𝜏𝑦𝑦 = −2𝜇 𝜕𝑣𝑦 𝜕(0) = −2𝜇 = 0 𝜕𝑦 𝜕𝑦 𝜏𝑧𝑧 = −2𝜇 𝜕𝑣𝑧 𝜕(0) = −2𝜇 = 0 ? ...
Purchase document to see full attachment
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

### Review

Anonymous
Nice! Really impressed with the quality.

Studypool
4.7
Indeed
4.5
Sitejabber
4.4