Cuprins
- 1. BASIC MATHEMATICS 11
- 2. FLUID PROPRIETIES 17
- 2.1 Compressibility 18
- 2.2 Thermal dilatation 20
- 2.3 Mobility 22
- 2.4 Viscosity 22
- 3. EQUATIONS OF IDEAL FLUID MOTION 29
- 3.1 Euler’s equation 29
- 3.2 Equation of continuity 32
- 3.3 The equation of state 34
- 3.4 Bernoulli’s equation 35
- 3.5 Plotting and energetic interpretation of Bernoulli’s equation for liquids 39
- 3.6 Bernoulli’s equations for the relative movement of ideal non-compressible fluid 40
- 4. FLUID STATICS 43
- 4.1 The fundamental equation of hydrostatics 43
- 4.2 Geometric and physical interpretation
- of the fundamental equation of hydrostatics 45
- 4.3 Pascal’s principle 46
- 4.4 The principle of communicating vessels 47
- 4.5 Hydrostatic forces 48
- 4.6 Archimedes’ principle 50
- 4.7 The floating of bodies 51
- 5. POTENTIAL (IRROTATIONAL) MOTION 57
- 5.1 Plane potential motion 59
- 5.2 Rectilinear and uniform motion 63
- 5.3 The source 66
- 5.4 The whirl 69
- 5.5 The flow with and without circulation around a circular cylinder 71
- 5.6 Kutta – Jukovski’s theorem 75
- 6. IMPULSE AND MOMENT IMPULSE
- THEOREM 77
- 7. MOTION EQUATION OF THE REAL FLUID 81
- 7.1 Motion regimes of fluids 81
- 7.2 Navier – Stokes’ equation 83
- 7.3 Bernoulli’s equation under the permanent regime of a thread of real fluid 87
- 7.4 Laminar motion of fluids 90
- 7.4.1 Velocities distribution between two plane parallel boards of infinit length 90
- 7.4.2 Velocity distribution in circular conduits 93
- 7.5 Turbulent motion of fluids 97
- 7.5.1 Coefficient in turbulent motion 99
- 7.5.2 Nikuradze’s diagram 102
- 8. FLOW THROUGH CIRCULAR CONDUITS 105
- 9. HYDRODYNAMIC PROFILES 113
- 9.1 Geometric characteristics of hydrodynamic profiles 113
- 9.2 The flow of fluids around wings116
- 9.3 Forces on the hydrodynamic profiles 119
- 9.4 Induced resistances in the case of finite span profiles 123
- 9.5 Networks profiles 125
Extras din curs
1. Basic mathematics
The scalar product of two vectors
and is a scalar.
Its value is:
. (1.1)
. (1.2)
The scalar product is commutative:
. (1.3)
The vectorial product of two vectors and is a vector perpendicular on the plane determined by those vectors, directed in such a manner that the trihedral , and should be rectangular.
. (1.4)
The modulus of the vectorial product is given by the relation:
. (1.5)
The vectorial product is non-commutative:
(1.6)
The mixed product of three vectors , and is a scalar.
. (1.7)
The double vectorial product of three vectors , and is a vector situated in the plane .
The formula of the double vectorial product:
. (1.8)
The operator is defined by:
. (1.9)
applied to a scalar is called gradient.
. (1.10)
scalary applied to a vector is called divarication.
. (1.11)
vectorially applied to a vector is called rotor.
. (1.12)
Operations with :
. (1.13)
. (1.14)
. (1.15)
When acts upon a product:
- in the first place has differential and only then vectorial proprieties;
- all the vectors or the scalars upon which it doesn’t act must, in the end, be placed in front of the operator;
- it mustn’t be placed alone at the end.
. (1.16)
. (1.17)
. (1.18)
, (1.19)
, (1.20)
, (1.21)
, (1.22)
. (1.23)
- the scalar considered constant,
- the scalar considered constant,
- the vector considered constant,
- the vector considered constant.
If:
(1.24)
then:
. (1.25)
The streamline is a curve tangent in each of its points to the velocity vector of the corresponding point .
The equation of the streamline is obtained by writing that the tangent to streamline is parallel to the vector velocity in its corresponding point:
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