physics

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2. Lesson Outline
• ideal fluid dynamics
• volume flux
• continuity equation
Source: V.van Gogh, Starry Night

3. I can describe the concept of ideal fluid
I can determine the volume flux in flowing fluid
I can solve the problem of continuity equation in flowing fluid

4. An ideal fluid is defined by the following set of characteristics. The
flow of the fluid must be
• steady
The velocity at any point in the flow does not change in time.
• incompressible
The density does not change with pressure.
• non-viscous
There are no sources of internal friction that could remove
energy from the flow.
• irrotational
An element (small piece) of the flow traces out a straight
path aligned with the fluid velocity, not a helical pattern
around it.
Ideal fluids

5. Ideal fluid flow is a simple, but
useful approximation to actual
fluid motion.
Arrows here represent the flow
velocity in a cross-sectional
cutout of the pipe.
The velocity is constant across the
area, there is no rotation, and no
drag (viscosity) near the edges of
the pipe.

6. STREAMLINE GEOMETRY

7. Small drag in streamlined position
Large drag in unstreamlined position
Both Images CC: BY-SA BoH (wimimedia commons) http://creativecommons.org/licenses/by-sa/3.0/

8. Turbulent flow: `vortex shedding’ around an obstacle
Steady (also called laminar) flow to the left of an island becomes
unsteady (or turbulent ) after passing by it. The grey scale image above
shows clouds in the atmosphere. Patches of the flow behind the obstacle
are spun up to create a series of vortices that alternately roll off, or ‘shed’,
from the top and bottom of the tube. The behavior downstream of the
tube is one of many examples of non-ideal fluid flow.
Island (from above)
ideal
fluid
flows
in
Source: NASA

9. Volume flux (Volume flow Rate)
Q = V/t
Q = Volume flux of fluid (m3/s)
V = Volume of flowing fluid (m3)
t = times taken by flowing fluid (s)

11. For a fluid of density r flowing through a pipe of cross-sectional
area A at speed v, the amount of mass Dm passing through a joint in
the pipe in a time interval Dt is given by
For regions of flow in which there are no sources or sinks of fluid,
the requirement that mass is neither created nor destroyed implies
that the product rAv is the same at all parts of the flow
Since an incompressible fluid has the same density at all points in the
flow (r=constant), then two locations (1 and 2) of a pipe with
different cross-sectional area will have the same volume flux.
Dm = r A v Dt
A1 v1 = A2 v2
r1 A1 v1 = r2 A2 v2
Conservation of mass for incompressible fluids