Transcript Document

Fluid mechanics 3.1 – key points
• A stationary fluid cannot withstand a shear stress
but deforms under the action of a shear.
• Fluids can be treated as continuous in time and
space.
• A fluid is shaped by external forces (i.e. a fluid
takes up the shape of its container)
• Gauge pressure equals the absolute pressure
minus the atmospheric pressure, or
• Absolute pressure equals the gauge pressure
plus the atmospheric pressure.
Unit 3
An Introduction to Mechanical
Engineering: Part One
Fluid mechanics 3.1 – key points
• Absolute pressure (relative to vacuum) and gauge
pressure (relative to atmospheric pressure) are
both used in engineering.
• Temperatures must be in kelvin in the perfect gas
equation.
• To convert from C to K, add 273.15.
• Pressure in a fluid is associated with molecular
motion.
• When pressure is constant over an area, F = pA .
Unit 3
An Introduction to Mechanical
Engineering: Part One
Fluid mechanics 3.1 – key points
• The perfect gas equation of state can be used to
obtain gas properties.
• Liquids can usually be treated as incompressible
but gases cannot.
Unit 3
An Introduction to Mechanical
Engineering: Part One
Fluid mechanics 3.1
Learning summary
By the end of this section you will be able to:
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Unit 3
calculate the density of an object from its mass and volume;
know the difference between and calculate gauge and absolute
pressure;
use the perfect gas equation of state to calculate the properties of
gases.
An Introduction to Mechanical
Engineering: Part One
Fluid mechanics 3.2 – key points
• In a fluid at rest, pressure acts equally in all
directions.
• Where a fluid is in contact with a surface, the
pressure gives rise to a force acting perpendicular
to the surface.
• In a fluid at rest, pressure is constant along a
horizontal plane.
• In a fluid at rest, pressure increases with depth
according to the relationship p = gh
• The pressure at the base of a column of fluid of
depth h is equal to the pressure at the top + gh
Unit 3
An Introduction to Mechanical
Engineering: Part One
Fluid mechanics 3.2 – key points
• Pressures can be measured by manometers.
• Surface tension can affect the readings of
manometers.
• On a submerged horizontal surface the pressure
is constant and the centre of pressure is also the
centre of area (centroid).
• On a submerged vertical surface the pressure
increases with depth and the centre of pressure is
below the centroid.
Unit 3
An Introduction to Mechanical
Engineering: Part One
Fluid mechanics 3.2 – key points
• On an inclined flat or curved surface the
horizontal force and its line of action is equal to
the horizontal force on the vertical projection of
the inclined or curved surface.
• On an inclined flat or curved surface, the vertical
force is equal to the weight of the volume of water
vertically above the surface and its line of action
passes through the centre of gravity of that
volume.
Unit 3
An Introduction to Mechanical
Engineering: Part One
Fluid mechanics 3.2 – key points
• A body fully immersed in a fluid experiences a
vertical upwards force equal to the weight of the
volume of fluid displaced.
• A floating body displaces its own weight in liquid.
Unit 3
An Introduction to Mechanical
Engineering: Part One
Fluid mechanics 3.2
Learning summary
By the end of this section you will be able to:
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Unit 3
determine the pressure at any depth below the surface of a liquid
at rest;
calculate the pressure difference indicated by a manometer;
calculate by integration the magnitude and line of action of the
force due to fluid static pressure on a submerged, flat, horizontal or
vertical surface;
evaluate the horizontal and vertical components of force on a
submerged, inclined, flat or simple curved surface and determine
the resultant force and line of action for some simple shapes;
calculate buoyancy forces on submerged and floating objects and
determine the conditions for equilibrium.
An Introduction to Mechanical
Engineering: Part One
Fluid mechanics 3.3 & 3.4 – key points
• A steady flow is one that does not change with
time.
• A uniform flow is one where the properties do not
vary across a plane or within a volume.
• A one-dimensional flow is one where flow
properties only vary in one direction.
• An ideal (inviscid) fluid has no viscosity, and is
incompressible. No real fluid is ideal but the
simplification is valid in some situations.
Unit 3
An Introduction to Mechanical
Engineering: Part One
Fluid mechanics 3.3 & 3.4 – key points
• For a steady flow, the law of conservation of mass
(continuity) means that the flow entering a volume
must equal the flow leaving a volume.
• The Euler equation is a differential equation for
the flow of an ideal fluid.
• The Bernoulli equation expresses the relationship
between pressure, elevation and velocity in an
ideal fluid for steady flow along a streamline.
• The Bernoulli equation can be expressed in three
ways, in terms of specific energy, pressure or
head.
Unit 3
An Introduction to Mechanical
Engineering: Part One
Fluid mechanics 3.3 & 3.4 – key points
• The Bernoulli equation can be used for real fluids
when losses due to friction are negligible and the
fluid is incompressible.
• Viscosity in a fluid creates frictional drag in a fluid
flow.
• The higher the viscosity of a fluid, the greater is
the resistance to motion between fluid layers, and,
for a given applied shear stress, the lower is the
rate of shear deformations between layers
Unit 3
An Introduction to Mechanical
Engineering: Part One
Fluid mechanics 3.3 & 3.4 – key points
• There are two fundamental types of fluid flow
laminar and turbulent. They can be characterized
by the Reynolds number of the flow.
• The steady flow energy equation can be applied
to the flow of real fluids and leads to the extended
Bernoulli equation that can be used to describe
the losses resulting from viscous friction in a flow.
• The Moody Chart can be used to estimate the
frictional losses in pipe and duct flows.
• The SFEE can be used to determine the
performance of a pump needed in a pipe system.
Unit 3
An Introduction to Mechanical
Engineering: Part One
Fluid mechanics 3.3 & 3.4
Learning summary
By the end of this section you will be able to:
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•
Unit 3
calculate the mass flowrate of a steady flow in a pipe or duct;
understand the three forms of the Bernoulli equation;
be able to apply the Bernoulli equation to calculate flows in pipes
including the performance of venturi, nozzle and orifice plate flow
meters and a pitot-static probe;
calculate the drag forces created by viscosity in thin films between
moving surfaces;
calculate the Reynolds number of flows in pipes and ducts and
determine whether the flow is likely to be laminar or turbulent;
estimate the pressure losses in flows in pipes due to friction;
calculate the pressures and flows in simple single pipe systems
accounting for losses due to friction in pipes and other components
of pipe systems;
calculate the performance of a pump needed in a simple pipe flow
system.
An Introduction to Mechanical
Engineering: Part One
Fluid mechanics 3.5 – key points
• The forces exerted by fluids when they change
velocity and direction can be evaluated using the
momentum equation derived from Newton’s
second law of motion.
• Control volumes are the easiest way to analyse
momentum flow problems.
• The linear momentum equation states that for a
steady flow: The force in a particular direction on
a control volume is equal to the rate of change in
momentum of the fluid flowing in that direction.
Unit 3
An Introduction to Mechanical
Engineering: Part One
Fluid mechanics 3.5 – key points
• The force on the control volume is the sum of all
the forces acting, including external pressure,
gravity and structural forces from solid objects
crossing the control volume boundaries.
Unit 3
An Introduction to Mechanical
Engineering: Part One
Fluid mechanics 3.5
Learning summary
By the end of this section you will be able to:
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Unit 3
calculate the forces generated when a fluid flow impinges on an
object or is constrained to change direction.
An Introduction to Mechanical
Engineering: Part One