a Parallel Plates Cone Plate (variable gap) (fixed gap)
a Parallel Plates (variable gap) Cone & Plate (fixed gap)
CONE AND PLATE Shear rate Y- a C Shear stress 3T O 2πR3 Newtonian fluids h=s 3Ta T Torque /8 2pR32
CONE AND PLATE W R a Shear stress T Torque R T Shear rate . = W a W 3 2 3 Newtonian fluids R T p a g s h
PARALLEL PLATES Shear stress 2+n R Shear rate R YR= h Newtonian fluids SR 2T 2Th and h= pR3 PR W
PARALLEL PLATES W R h Shear rate h R R W Shear stress ln ln 3 2 3 d d T R T R Newtonian fluids s R = 2T pR 3 and h = 2Th pR 4W
CONCENTRIC CYLINDERS T 01= 2pR2h “For narrow gaps'” R where R2≈Rl R 。。+ R R2-R
W CONCENTRIC CYLINDERS 1 = T 2pR1 2h h R1 R2 2 1 1 R2 R1 R R R where W “For narrow gaps
Tube Flow (- du(r) shear dr shear rate stress profile profile u(r） parabolic velocity profile The physical parameters relating to flow in a tube:flow rate pressure drop P along the pipe of length L and radius a
Newtonian Fluids gú w = 4Q pa 3 w = Pa 2L gú = Ppa 4 8LQ gú w and s w are values or shear rate and stress at the wall of the tube. At the center of the tube : gú o and s o = 0 Tube Flow u(r) = P 4hL a 2 - r 2 ( )