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HYDRAULICS

INTRODUCTON

OBJECIVE:

study of mechanical behavior (laws of equilibrium and motion of liquids)

study of mechanical behavior of solids (pipes, reservoirs, tanks) acted up by liquids

DOMAIN OF APPLICABILITY:

dams (hydrotechnics)

water supply systems including transportation, distribution, storage, treatment, inside

utilities

sewerage systems including the inside sewerage, street sewerage, filtering, spillway into anatural vector

regularization of natural courses (rivers, flows, streams) aiming at protection of naturalbanks and engineering works

hydraulic engines

underground flows

navigable canals

RELATIONS WITH OTHER SUBJECTS:

mechanics of continuum, namely fluid mechanics (through the general laws of

mechanics)

physics through the fluid properties

strength of materials

mathematics

mechanical engineering

OBJECTIVES OF OUR SUBJECTS:1. hydrostatics behavior of liquids and solids acted upon by liquids2. hydrodynamics (behavior in motion of liquids and solids acted upon by liquids

Hydrostatics includes all the engineering works that are related with the liquid in itsresting state: tanks vessels, pools.

Hydrodynamics includesall the engineering works related with the liquid in its motion:pipes, canals, rivers, underground flows.

SUBJECT STRUCTURE:

Theoretical background (general laws of Fluid Mechanics)

Engineering applications in Civil Engineering:

o design of construction element acted upon by liquidso design of underground water resourceso design of municipal works (water supply and water sewerage system)

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SHORT HISTORICAL PRESENTATION OF HYDRAULICSWater has been used by people since the beginning of human history: as a vital element of life

and later as a tool to improve the quality of life (transports, irrigation, water supplies).

The first theoretical contribution in Hydraulics belongs to Archimedes (250 BC) under the nameoffloating bodies. Another landmark in this science has been the work of Leonardo da Vinci:On Motion and Measurement of Water. D. Bernoulli and Leonard Euler established the basis of

classical hydrodynamics, at the beginning of the 18th

century.

Liquid Modeling

Hydraulics as any other science needs in its study a mechanical model of liquid behavior. The

model is build up from practical experiments concerning liquids. The conclusion drawn from thepractical experiments have been synthesized into several hypotheses regarding the liquid

behavior. Hydrostatics uses only one hypothesis: the hypotheses of continuum medium. The

objective of Hydrostatics (the stress state of the liquid) can be completely described using thishypothesis only. The models of Hydrodynamics have been continuously improved as the stress

state in motion is more complex. During the history, 3 models have been used in Hydrodynamics:

the model of ideal fluid, assuming that the fluid has no viscosity and compressibility;

the model of viscous fluid;

the model of viscous and turbulent fluid;To each mechanical model, a mathematical instrument is associated.

HYDROSTATICS

Physical properties of liquids

In Hydraulics fluid is any liquid or gaseous body which presents a great mobility of its particles

without being significantly aced upon.

The property is calledfluidity.

The unit weightis the second property of a liquid.

V

G

unit weight; []=ML-2T-2

Gliquid weight; [G]=MLT-2

[V]liquid volume; [V]=L3

In the day by day use []=FL-3

The unit weight depends on the: liquid nature, temperature, pressure. For water at 4C and normal

atmosphere pressure (1 at) =9810 N/m3. This value is used in the current civil engineering

design.

The density is next liquid property.

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V

M

Mliquid mass[]=ML

-3

[M]=M

In terms of, one gets:g

g

The same dependency of on temperature, pressure and liquid nature as of may be mentioned.

The technical value of for water in civil engineering is 1000 kg/m3.

Compressibility is the next property. It is defined by rationV

dVwhere Vis the initial volume and

dVis change in the volume.

pdV

V-dV

From Physics we have:

dpVdV ;

whereis the cubic compressibility coefficient and dp is the change in the pressure. For the usualliquidsis very small and therefore the hypothesis of incompressibility of liquids is fairly true.

The next property is viscosity. It is the liquid property through which at the liquid interface with

another medium, tangential stresses contrary to the liquid flow are born.

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left bank

rigth bankbottom level

vv

*velocity distribution due to viscosity*

Another liquid property is the capillarity (see Physics) expressed through the capillary tension .

The capillary tension depends on the liquid nature.

V-dV

liquid(water)

capillary tube

The capillary height h depends of liquid nature and capillary tube diameter d

From the equilibrium condition of liquid spout, (coloana de lichid), one gets:

hd

d4

2

; []=daN/m; For water =0,0077 daN/m

It yields that2

30mmdh

The last two properties are related to each other, and are absorption and cavitation.

The absorption is the liquid property to store its mass a certain quantity of air, depending on thetemperature and pressure.

The cavitation is the opposite phenomenon to absorption: the liquid property to eliminate air from

its mass due to the temperature and pressure variations. Under the usual conditions (temperatureand pressure), the water contents about 2% air of its volume

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PART ONE: HYDROSTATICS

1.1.Fundamental law of hydrostatics

Between the particles (either in motion or in rest), there are mutual actions which are

mechanically equivalent to link forces between particles. Their presence gives birth to tensionstate of liquid which is easily provided by the action of liquid on the vessels.

(P)

(A)(V) (V)

(P)

Aliquid surface along plane (P)

A elementary surface of liquid along plane (P) around point M

F elementary force of liquid acting on A force

F total force of liquid acting on

To keep the liquid in form from Fig. 1.1.b. we have to act along plane (P) with the force F.

Taking the limit for A (elementary surface), one gets

dA

Fd

A

Fp

Alim

0

where p is hydrostatic pressure or in terms of strength of materials, p is a unit stress specific toliquids.

More explicitly: the hydrostatics pressure p is a stress state around point M of the liquid due to

massic forces, link forces, exterior forces, surface forces.

Properties of hydrostatic pressure (h p) for water:The h.p is always compression

Around point M, h.p is constant whatever its directions are

h p is always normal (l) to the surface it is acting on

h.p is linearly dependent on the depth of point M in the water

any exterior action acting on the water is totally transmitted to any point M of the liquidand along all directions defined around M.