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Biofluid Mechanics: An Introduction to Fluid Mechanics, Macrocirculation, and Microcirculation, 3rd Edition (2021)

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Chapter 22.1: For the velocity distribution𝑣𝑥=5𝑥,𝑣𝑦=−5𝑦,𝑣𝑧=0,determine the acceleration vector.Also, determine whether this velocity profile has a local and/or convective acceleration.𝑎⃗=𝜕𝑣⃗𝜕𝑡+𝑣𝑥𝜕𝑣𝜕𝑥+𝑣𝑦𝜕𝑣𝜕𝑦+𝑣𝑧𝜕𝑣𝜕𝑧𝑣⃗=5𝑥𝑖̂−5𝑦𝑗̂𝜕𝑣𝜕𝑡=0→𝑛𝑜𝑙𝑜𝑐𝑎𝑙𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝜕𝑣𝜕𝑥=5𝜕𝑣𝜕𝑦=−5𝜕𝑣𝜕𝑧=0𝑎⃗=0+5𝑥(5)𝑖̂−5𝑦(−5)𝑗̂+0=25𝑥𝑖̂+25𝑦𝑗̂→𝑜𝑛𝑙𝑦𝑐𝑜𝑛𝑣𝑒𝑐𝑡𝑖𝑣𝑒𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛2.2: Consider a velocity vector𝑣=(𝑥𝑡2−𝑦)𝑖⃗+(𝑥𝑡−𝑦2)𝑗⃗. (a) Determine if this flow is steady(hint: no changes with time). (b)Determine if this is an incompressible flow (hint: check if∇∙𝑣=0).(𝑎)𝑣=(𝑥𝑡2−𝑦)𝑖⃗+(𝑥𝑡−𝑦2)𝑗⃗

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