1.6 An incompressible Newtonian fluid flows in the z-direction in space between two par- allel plates that are separated by a distance 2B as shown in Figure 1.3(a). The length and the width of each plate are L and W, respectively. The velocity distribution under steady conditions is given by JAP\B² Vz = 2µL a) For the coordinate system shown in Figure 1.3(b), show that the velocity distribution takes the form JAP|B²| Vz = 2µL Problems 11 "L. 2B --– € (a) 2B (b)

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1.6 An incompressible Newtonian fluid flows in the z-direction in space between two par-
allel plates that are separated by a distance 2B as shown in Figure 1.3(a). The length and
the width of each plate are L and W, respectively. The velocity distribution under steady
conditions is given by
JAP|B²
Vz =
2µL
B
a) For the coordinate system shown in Figure 1.3(b), show that the velocity distribution
takes the form
JAP|B?
v, =
2μL
Problems
11
- 2B --– €.
(a)
2B
(b)
Figure 1.3. Flow between parallel plates.
b) Calculate the volumetric flow rate by using the velocity distributions given above. What
is your conclusion?
2|A P|B³W
Answer: b) For both cases Q =
3µL
Transcribed Image Text:1.6 An incompressible Newtonian fluid flows in the z-direction in space between two par- allel plates that are separated by a distance 2B as shown in Figure 1.3(a). The length and the width of each plate are L and W, respectively. The velocity distribution under steady conditions is given by JAP|B² Vz = 2µL B a) For the coordinate system shown in Figure 1.3(b), show that the velocity distribution takes the form JAP|B? v, = 2μL Problems 11 - 2B --– €. (a) 2B (b) Figure 1.3. Flow between parallel plates. b) Calculate the volumetric flow rate by using the velocity distributions given above. What is your conclusion? 2|A P|B³W Answer: b) For both cases Q = 3µL
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