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 andthe width of each plate are L and W, respectively. The velocity distribution under steadyconditions is given byJAP|B²Vz =2µLBa) For the coordinate system shown in Figure 1.3(b), show that the velocity distributiontakes the formJAP|B?v, =2μLProblems11- 2B --– €.(a)2B(b)Figure 1.3. Flow between parallel plates.b) Calculate the volumetric flow rate by using the velocity distributions given above. Whatis your conclusion?2|A P|B³WAnswer: b) For both cases Q =3µL

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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 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)

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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Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.

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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

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