Page 48 - Fluid mechanics, heat transfer, and mass transfer

FLOW PHENOMENA 25

and r and m are fluid density and viscosity,
respectively.

Superficial velocity; V ¼ «v; ð2:15Þ
0
where v is the actual velocity.
ðiiiÞ Impeller Reynolds number;
2
N Re ¼ D Nr=m; ð2:16Þ
Equivalent diameter for annulus.
FIGURE 2.4
where D is the impeller diameter and N is rpm.
2 2
equivalent diameter; D e ¼ 4½pðD d Þ=4Š=pðD þ dÞ . What is boundary layer? Illustrate.
& Flow far from the surface of a solid object is inviscid
¼ D d: ð2:9Þ
and effects of viscosity are manifest only in a thin
layer near the surface where steep velocity gradients
Rectangular duct:
occur.
D e ¼ 4LW=2ðL þ WÞ; ð2:10Þ
& Boundary layer is where the fluid is influenced by
where L is the length and W is the width of the duct. friction with its boundaries. Flow is zero at the
boundary and increases away from the boundary
Square duct: until it reaches the mean or maximum velocity of
D e ¼ L: ð2:11Þ the flow. The zone of flow velocity increase is called
boundary layer.
. Give the equation for hydraulic radius of a packed & In other words, the thin layer where velocity de-
bed. creases from the inviscid potential flow velocity to
r H ¼ðvolume of voidsÞ=ðvolume of bedÞ= zero at solid surfaces is called boundary layer.
& Development of boundary layer is illustrated in
ðwetted surfaceÞ=ðvolume of bedÞ¼ «=a; ð2:12Þ Figure 2.5.
. State Bernoulli’s principle.
where a is 6(1 «)/D p ¼ [«/6(1 «)]D p .
& Bernoulli’s principle states that in an ideal fluid with
. How is Reynolds number defined for (i) noncircular
no work being performed on the fluid, an increase in
conduits, (ii) packed beds, and (iii) mixing? velocity occurs simultaneously with decrease in
& ðiÞ N Re ¼ D e r=m; ð2:13Þ
pressure or a change in the gravitational potential
energy of the fluid.
where D e is the equivalent diameter of the non-
& This principle is a simplification of Bernoulli’s equa-
circular flow conduit.
tion, which states that the sum of all forms of energy
0
ðiiÞ N Re;p ¼ D p V =½ð1 «ÞmŠ ðErgun’s definitionÞ; in a fluid flowing along an enclosed path (a stream-
r
ð2:14Þ line) is the same at any two points in that path.
& In fluid flow with no viscosity, and, therefore, one in
where D p is the particle/packing diameter, V is which a pressure difference is the only accelerating
0
the superficial velocity, « is the void fraction, force, it is equivalent to Newton’s laws of motion. It

Development of boundary layer.
FIGURE 2.5