Student Handout 19 2014

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  • shell balances

    CHEE 3363Spring 2014Handout 19

    Reading: Fox 8.1--8.4

  • Learning objectives for lecture

    State the criterion for the transition from laminar to turbulent

    2

  • Reynolds number Re =

    laminarturbulent

    This transition is approximate

    3

  • [

    yx +yx

    y

    (

    dy

    2

    )]

    dx dz

    [

    yx +yx

    y

    (

    dy

    2

    )]

    dx dz

    [

    p +p

    x

    (

    dx

    2

    )]

    dy dz

    [

    p +p

    x

    (

    dx

    2

    )]

    dy dz

    p, yx

    (shell balance) using the macroscopic equationsh

    x

    y

    4

  • 5

  • 3

    yof x

    6

  • 4

    7

  • 5L

    8

  • 6

    9

    y in

  • 7

    stationary top plate U = 0

  • 8

    L

  • 9

    y in

  • p2r dr

    (

    p +p

    xdx

    )

    2r dr

    rx2r dx

    (

    rx +drx

    drdr

    )

    2(r + dr) dx

    p, rx

    h xr

    2R

    In xexcept surface force term FSx vanish

    annulus

  • 2

  • 3

    function only of x(uniform pressure at each section)

    function only of r(fully developed)

  • 4

  • 5

  • r = 0

    6

    r in

    maximum at

  • Goal

    Need to account for losses due to friction

    system

  • shear force

    20

    (2) (3)

  • equations of motion

    boundary layer

    Entrance length 2

    (2) (3)