Fundamentals of Ideal Fluid

BPS1133 Engineering Science
Fundamentals of Ideal Fluid

Phases of Matter
Solid Liquid Gas
• Fixed shape, • does not • neither fixed
fixed size maintain fixed shape nor fixed
shape (take the volume (it’s
shape of its expand to its
container) container)
• does not • also not readily • compressible
readily change in compressible
shape or volume (volume can
when force is change with
applied large force)
Fluid’s definition:
“ a substance which has no definite shape and

has the ability to flow. Such as liquid and
gas”
There are 4 basic factors governing the pressure within
fluids:
i) The pressure at a given depth in a fluid is equal in all
directions.(Figure a)
ii) The pressure at a given depth in a fluid is independent
of the shape of the container in which the fluid is held.
(Figure b)
i) Pressure acts at right angles to the surface containing
the fluid. (Figure c)
ii) When a pressure is applied to a fluid, this pressure is
transmitted equally in all directions. (Figure d)
• It is more useful to consider density and pressure
for a fluid, which may take different values for
different parts of the fluid.
• The SI unit of density is kg/m3 .
• The SI unit of pressure is N/m2(pascal).
• The pressure at a depth h below the surface of the
liquid is due to the weight of the liquid above it. We
can calculate by
Example:
Atmospheric Pressure and Gauge Pressure
• Most pressure gauges measure the pressure above

the atmospheric pressure – this is called the gauge
pressure.
• Atmospheric pressure, is the pressure within the
atmosphere of Earth.
• The absolute pressure is the sum of the
atmospheric pressure and the gauge pressure.
Absolute pressure = atmospheric pressure + Gauge pressure
Example:
Fluids at Rest
• The pressure at a point in a fluid in static

equilibrium depends on the depth of that point but
not on any horizontal dimension of the fluid or its
container.
• If y1 is at the surface and y2 is at a depth h below
the surface, where po is the pressure at the surface,
and p the pressure at depth h.
Ideal Fluid
• Consider a hypothetical fluid having a zero
viscosity ( μ = 0). Such a fluid is called an ideal
fluid and the resulting motion is called
as ideal or inviscid flow. In an ideal flow, there is
no existence of shear force because of vanishing
viscosity
• All the fluids in reality have viscosity (μ > 0) and

hence they are termed as real fluid and their
motion is known as viscous flow.
• Under certain situations of very high velocity flow
of viscous fluids, an accurate analysis of flow field
away from a solid surface can be made from the
ideal flow theory.
Ideal Fluids in Motion
• Realistic fluids are complicated. We usually study

‘ideal’ fluids as a model to obtain many useful
results. An ideal fluid is a fluid with the following
four assumptions:
Steady flow: In steady (or laminar) flow, the
velocity of the moving fluid at any fixed point does
not change with time.
Incompressible flow: We assume, as for fluids at
rest, that our ideal fluid is incompressible; that is,
its density has a constant, uniform value.
Ideal Fluids in Motion
Nonviscous flow: The viscosity of a fluid is a

measure of how resistive the fluid is to flow;
viscosity is the fluid analog of friction between
solids. An object moving through a nonviscous
fluid would experience no viscous drag force—that
is, no resistive force due to viscosity; it could move
at constant speed through the fluid.
Irrotational flow: In irrotational flow a test body
suspended in the fluid will not rotate about an
axis through its own center of mass
The Motion or Flow Fluids can get Pretty complicated. We
simplify with a model called IDEAL Fluids.
IDEAL Fluids REAL FLUIDS
Always: Incompressible Could be compressible
(constant density)
Always: LAMINAR Flow (steady) Could have Turbulent Flow
(if too fast)
Always: Non-viscous Defining Characteristic: Viscous
flow
Viscosity = Thickness = Fluid
friction
e.g. water e.g. All fluid available in nature
Pascal’s Principle
• If an external pressure is applied to a confined

fluid, the pressure at every point within the fluid
increases by that amount.
• This principle is used, for example, in hydraulic
lifts and hydraulic brakes.
Buoyancy and Stability
Buoyancy is ultimately what

make things float. Force FB is
equal only to the displaced
volume fgVdisplaced.
Three scenarios possible

1. body<fluid: Floating
body
2. body=fluid: Neutrally
buoyant
3. body>fluid: Sinking
body
Archimedes’ Principle
• When a body floats in a fluid, the magnitude Fb of
the buoyant force on the body is equal to the
magnitude Fg of the gravitational force on the body.
• when a body floats in a fluid, the magnitude Fg of

the gravitational force on the body is equal to the
weight mfg of the fluid that has been displaced by
the body, where mf is the mass of the fluid
displaced.
Fluids in Motion
• If the flow of a fluid is smooth, it is called
streamline or laminar flow (a).
• Above a certain speed, the flow becomes turbulent
(b). Turbulent flow has eddies; the viscosity of the
fluid is much greater when eddies are present.
• Eddy is the swirling of a fluid and the reverse current created
when the fluid flows past an obstacle.
Equation of Continuity
• The mass flow rate is the mass that passes a given
point per unit time.
• The flow rates at any two points must be equal, as
long as no fluid is being added or taken away.
• This gives us the equation of continuity:
• If the density doesn’t change – typical for liquids
this simplifies to . Where the pipe is
wider, the flow is slower.
The Equation of Continuity
• When the end of a hose is partially closed off,
reducing its cross-sectional area, the fluid velocity
increases. This kind of fluid behavior is described
by the equation of continuity.
Bernoulli’s Principle
“Within a horizontal flow of fluid, points of

higher fluid speed will have less pressure than
points of slower fluid speed”
“Bernoulli's equation can be viewed as a

conservation of energy law for a flowing fluid”
Bernoulli’s Equation
• A fluid can also change its

height. By looking at the
work done as it moves, we
find:
• This is Bernoulli’s
equation. One thing it tells
us is that as the speed
goes up, the pressure goes
down
Applications of Bernoulli’s
Principle
• A venturimeter can be used to measure fluid flow
by measuring pressure differences.
Applications of Bernoulli’s
Principle
• Air flow across the top helps smoke go up a
chimney, and air flow over multiple openings can
provide the needed circulation in underground
burrows.
Thank You

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BPS1133 Engineering Science

Fundamentals of Ideal Fluid

“ a substance which has no definite shape and

• Most pressure gauges measure the pressure above

• The pressure at a point in a fluid in static

• All the fluids in reality have viscosity (μ > 0) and

• Realistic fluids are complicated. We usually study

Nonviscous flow: The viscosity of a fluid is a

• If an external pressure is applied to a confined

Buoyancy is ultimately what

Three scenarios possible

• when a body floats in a fluid, the magnitude Fg of

“Within a horizontal flow of fluid, points of

“Bernoulli's equation can be viewed as a

• A fluid can also change its

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