▁= ▁blood ▁flow ▁( ml / s ) ▁ ▁A ▁= ▁cross ▁section al ▁area ▁( cm 2 ) ▁ ▁Tur bul ence ▁ ▁Blood ▁flow ▁is ▁also ▁affected ▁by ▁the ▁smooth ness ▁of ▁the ▁vessels , ▁resulting ▁in ▁either ▁tur bul ent ▁( cha otic ) ▁or ▁l amin ar ▁( sm ooth ) ▁flow . ▁Sm ooth ness ▁is ▁reduced ▁by ▁the ▁bu il dup ▁of ▁fat ty ▁depos its ▁on ▁the ▁ar ter ial ▁walls . ▁ ▁The ▁Reyn old ' s ▁number ▁( den oted ▁NR ▁or ▁Re ) ▁is ▁a ▁relationship ▁that ▁helps ▁determine ▁the ▁behavior ▁of ▁a ▁fluid ▁in ▁a ▁t ube , ▁in ▁this ▁case ▁blood ▁in ▁the ▁vessel . ▁ ▁The ▁equation ▁for ▁this ▁dimension less ▁relationship ▁is ▁written ▁as : ▁▁▁ ρ : ▁density ▁of ▁the ▁blood ▁ ▁v : ▁mean ▁velocity ▁of ▁the ▁blood ▁ ▁L : ▁characteristic ▁dimension ▁of ▁the ▁vessel , ▁in ▁this ▁case ▁diameter ▁▁ μ : ▁vis cos ity ▁of ▁blood ▁ ▁The ▁Reyn old ' s ▁number ▁is ▁directly ▁proportional ▁to ▁the ▁velocity ▁and ▁diameter ▁of ▁the ▁t ube . ▁Note ▁that ▁NR ▁is ▁directly ▁proportional ▁to ▁the ▁mean ▁velocity ▁as ▁well ▁as ▁the ▁diameter . ▁A ▁Reyn old ' s ▁number ▁of ▁less ▁than ▁ 2 3 0 0 ▁is ▁l amin ar ▁fluid ▁flow , ▁which ▁is ▁character ized ▁by ▁constant ▁flow ▁motion , ▁whereas ▁a ▁value ▁of ▁over ▁ 4 0 0 0 , ▁is ▁represented ▁as ▁tur bul ent ▁flow . ▁Due ▁to ▁its