Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

18.3 Nonlinear Models 595

2

5

Polynomial Functions

Laminar Fluid Velocity Inside a Pipe For those of you who are planning to become an aero-

space, chemical, civil, or mechanical engineer, later in your studies you will

take a fluid mechanics class. In that class, among other topics, you will

learn about the flow of fluids in pipes and conduits. For a laminar flow, the

velocity distribution — how fluid velocity changes at a given cross-

section — inside a pipe is given by

(18.6)

where

u(r)fluid velocity at the radial distancer(m/s)

Vccenter line velocity ( m/s)

rradial distance measured from the center of the pipe ( m)

Rradius of the pipe ( m)

The velocity distribution for a situation whereVc0.5 m/s andR0.1 m is shown in

Figure 18.6. From Figure 18.6, it is evident that the velocity equation is a nonlinear

u 1 r 2 Vc c 1 a

r

R

b

2

d

Velocity,u(r) (m/s)

0.6

0.5

0.4

0.3

0.2

0.1

0.0

0.15 0.10 0.05 0 0.05

r

0.10

Slope

Slope

0.15

Radial distance from the center of pipe, r (m)

Slope

ru (r)

0.1 0

0.09 0.095

0.08 0.18

0.07 0.255

0.06 0.32

0.05 0.375

0.04 0.42

0.03 0.455

0.02 0.48

0.01 0.495

0 0.5

0.01 0.495

0.02 0.48

0.03 0.455

0.04 0.42

0.05 0.375

0.06 0.32

0.07 0.255

0.08 0.18

0.09 0.095

0.1 0

■Figure 18.6 An example of fluid velocity distribution inside a pipe.

R

r

Vc

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