Ch11 Fluid Mechanics

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Fluid Mechanics

Introduction

Fluid mechanics: the branch of physics (or applied mechanics) which isconcerned with the behavior offluids at restor in motion.

Both liquids and gases are fluids.

Fluid mechanics rinci les and conce ts are often involved in the stud andanalysis of thermal systems

This field includes many problems: blood flow in the capillaries, flow of airaround an airplane, flow of crude oil in oil pipelines, etc.

Fluid mechanics is divided into: fluid statics (studying fluids at rest) andfluid dynamics (studying fluids in motion).

Fluid Statics

Thermo-fluid Engineering (MEC 2920) 1

The only forces of interest are due to the pressure acting on the surfaces of afluid element and the weight of the fluid element.

Investigation of pressure and its variation throughout a fluid at rest, and the

effect of pressure on submerged or partially submerged surfaces.

Fluid Statics

Pressure Variation in a Fluid at Rest

Pressure: the normal force per unit area at a given point acting on a givenplane within a fluid mass of interest.

Consider a small, stationary element of fluid at some arbitrary position withina mass of fluid

There are two types of forces acting on this element:

surface forces due to the pressure, and

body force equal to the weight of the element, which can be written as



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Fluid Statics

From the equilibrium of the fluid element,

Therefore, we obtain


Fluid Statics

for incompressible fluid ( = constant)

The distance h = z2 z1 is called thepressure head



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Fluid Statics

The hydrostatic pressure distribution p at any depth h below the free surface of aliquid is given by


Fluid Statics



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Measurement of Pressure

absolute pressure or gage pressure.

Absolute pressure is measured relative to absolute zero pressure (+).

Gage pressure is measured relative to the local atmospheric pressure (+/).

Fluid Statics

.

Thermodynamic analyses use absolute pressure.

However, most fluid mechanics analyses use gage pressure for convenience


Fluid Statics

The measurement of atmospheric pressure is usually accomplished with a

mercury barometer



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Manometry

A standard technique for measuring pressure which uses liquid columns invertical or inclined tubes.

Pressure measuring devices based on this technique are called manometers.

The mercury barometer is an example of one type of manometer

Fluid Statics

Two other common types of manometers include thepiezometertube and theU-tube manometer.

Piezometer Tube Simplest type of manometer consisting of a vertical tube, open at the top, and

attached to a container in which the pressure is to be measured


Absolute pressure

Gauge pressure

Disadv.: p1 must be greater than p0 , p1-p0 should be small, fluid must be liquid

U-Tube Manometer

To overcome the difficulties associated with piezometer, another type ofmanometer that is widely used consists of a tube formed into the shape of a U

The fluid in the manometer is called thegage fluid.

Fluid Statics

p2 = p3 p1 + 1 h1 = p0 + 2 h2


Gage pressure


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Fluid Statics

The U-tube manometer is also widely used to measure the difference inpressure between two containers or two points in a given system.

p2

= p3

pA 1 1 = pB 3 3 2 2


Specific Gravity

The specific weight, , of a liquid such as the gage fluid is often expressed in termsof the specific gravity, SG, by the following relationship (water = 1000 kg/m

3)

Fluid Statics

Mechanical and Electronic Pressure Measuring Devices

Manometers are suitable to measure very high, or rapidly changing pressures.

They, also, require the measurement of one or more column heights.

Numerous other pressure-measuring instruments have been developed.

structure will deform. This deformation is related to magnitude of pressure.

Bourdon Pressure Gage

The most common type of its type.

The essential mechanical element in this gage is bourdon tube.

As the pressure within the tube increases, the tube tends to straighten

This can be translated into the motion of a pointer on a dial.

The indicated pressure is gage pressure, which can be positive or negative.



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Fluid Statics

Pressure Transducer

For many applications in which pressure measurements are recorded, the pressuremust be measured with a device that converts pressure into an electrical output.

This type of pressure measuring device is called apressure transducer

Many different designs exists.


Hydrostatic Force on a Horizontal Plane Surface

If a surface is submerged in a fluid, forces acts on the surface due to the fluid.

Determining these forces is important to design many hydraulic structures.

In fluids at rest, the force must beperpendicularto the surface.

Fluid Statics

, .

Horizontal submerged surface uniform pressure , the magnitude ofthe resultant force is FR = p A , p = h (resultant force acts through thecentroid of the area).

Vertical submerged surface pressure is not uniform p = h



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Hydrostatic Force on an Inclined Plane Surface

A submerged surface of arbitrary shape makes an angle with the free surface.

Determine the resultant force:

Direction, Location, Magnitude

The force actin on dA is dF= hdA

Fluid Statics

dFis perpendicular to the surface.

Integrating over the surface, we get

If is constant



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Fluid Statics

yc is the y-coordinate of the centroid measured from x axis, passing through O

Then,

Resultant hydrostatic force will be

the magnitude of the resultant force is


the area multiplied by the total area

Fluid Statics

The point through which the resultant force acts is called thecenter of pressure

The y-coordinate of the resultant force, yR, can be determined by summation ofmoments around the x-axis. That is

I is the second moment of the areaA with es ect


xc to an axis passing through the centroid ofA.


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Fluid Statics


Fluid Statics



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Fluid Statics


Fluid Statics

Buoyancy

When a body is completely or partially submerged in a fluid, the resultant

fluid force acting on the body is called the buoyant force.

A net upward vertical force results from the pressure increase with depth

Pressure forces actin from below are lar er than those from above.

From elementary physics, the buoyant force is given by

Example:

The buoyant force has a magnitude equal to the weight of the fluid displacedby the body, and is directed vertically upward[Archimedes Principle]


.m and weighing 8.50 kN that is anchored to the seafloor with a cableAssume that the buoy is completely immersed.In this case, what would be the tension in the cable?

Ch11 Fluid Mechanics

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