ENGR2000 Lecture Notes - Lecture 1: Reynolds Number, Well-Order, Leading Edge

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2 Jul 2018
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2nd-Year Fluid Mechanics, Faculty of Science & Engineering, Curtin University
ENGR2000: FLUID MECHANICS
For Second-year Chemical, Petroleum, Civil & Mechanical Engineering
FLUID MECHANICS LECTURE NOTES
CHAPTER 1: THE CHARACTERISATION OF FLUID FLOWS
The essential difference between Fluids and Solid Mechanics is that a fluid at
rest cannot support a shear force. Moreover, it cannot support a direct stress
(a pressure in fluid mechanics) unless the direct stress is exactly balanced by
gravitational forces - as occurs in Hydrostatics (see Chapter 2). If a shear
and/or a direct stress is applied to a ‘lump’ of fluid it will deform by flowing.
To complicate matters, the stresses in a fluid are determined by the fluid
flow. It is this inter-relation between stress (force) and flow that makes
Fluid Mechanics (or Dynamics) particularly challenging.
At the heart of this unit is the inter-relation between forces and fluids; how
forces cause fluids to move (and how such forces are created by, for example
pumps) and what are the forces exerted by moving fluids. This understanding
provides the foundation for engineers to use these effects in a wide range of
applications such as aircraft flight, the pipe-work system in a oil-processing
plant or the design of buildings able to withstand hurricane-force winds, to
name but a few examples.
The approach to this study generally follows that adopted in Solid Mechan-
ics - consideration of stresses, free bodies (isolating a part of the continuous
structure/flow-field) which are here called control volumes coupled to dy-
namics (Newton’s laws, conservation principles, relative motion etc).
This chapter serves to generate a basic awareness of the different types of
fluid flow in preparation for more detailed coverage in later chapters. The
special case of fluid mechanics when there is no flow - called Hydrostatics -
is addressed in Chapter 2.
Chapter 1 Page 1
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2nd-Year Fluid Mechanics, Faculty of Science & Engineering, Curtin University
1.1 Flow Fields
A flow field describes the motion of fluid in a given region. The general
character of the motion is illustrated by streamlines which are lines along
which an imaginary particle (eg. a cork or a drop of coloured ink) would
move. The simplest flow field is that of uniform flow seen in Fig 1.1,
occurring in an infinite region.
FIGURE 1.1: Unbounded uniform flow
To mathematically describe the flow anywhere in a region, we list the flow
properties at each point in the region. At present we shall focus on the
velocity, v(a vector), of the fluid at any location in the flow field. Of course,
other properties (eg. density, pressure, temperature) may vary in the region
of flow. Writing the flow velocity in component form, then:
v(x, y) = u(x, y)i+v(x, y)j(1.1)
where uand vare the flow speeds in the x- and y-directions. For uniform
flow (Fig 1.1), u=U(constant) and v= 0; hence the name... no variation
with xor y.
Chapter 1 Page 2
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2nd-Year Fluid Mechanics, Faculty of Science & Engineering, Curtin University
Now place an object (a cylinder) in the uniform flow. For low U, the flow
field would look like Fig 1.2.
FIGURE 1.2: Low-speed flow round a cylinder in the absence of friction (viscosity)
The flow velocity at a point is tangential to the streamline which passes
through that point: spatial dependence (ie. on xand y) is now evident.
Note that both the flow velocity, v, and the flow speed (|v|=u2+v2) can
change along a streamline. The equation for a streamline can be found by
considering the motion of an imaginary particle along a streamline as shown
in Fig 1.3.
Chapter 1 Page 3
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