![]() | This article includes a list of general
references, but it lacks sufficient corresponding
inline citations. (March 2010) |
The theory of sonics is a branch of continuum mechanics which describes the transmission of mechanical energy through vibrations. The birth of the theory of sonics [1] is the publication of the book A treatise on transmission of power by vibrations in 1918 by the Romanian scientist Gogu Constantinescu.
ONE of the fundamental problems of mechanical engineering is that of transmitting energy found in nature, after suitable transformation, to some point at which can be made available for performing useful work. The methods of transmitting power known and practised by engineers are broadly included in two classes: mechanical including hydraulic, pneumatic and wire rope methods; and electrical methods....According to the new system, energy is transmitted from one point to another, which may be at a considerable distance, by means of impressed variations of pressure or tension producing longitudinal vibrations in solid, liquid or gaseous columns. The energy is transmitted by periodic changes of pressure and volume in the longitudinal direction and may be described as wave transmission of power, or mechanical wave transmission. – Gogu Constantinescu [2] [3]
Later on the theory was expanded in electro-sonic, hydro-sonic, sonostereo-sonic and thermo-sonic. The theory was the first chapter of compressible flow applications and has stated for the first time the mathematical theory of compressible fluid, and was considered a branch of continuum mechanics. The laws discovered by Constantinescu, used in sonicity are the same with the laws used in electricity.
The book A treatise on transmission of power by vibrations has the following chapters:
George Constantinescu defined his work as follow.
If v is the velocity of which waves travel along the pipe, and n the number of the revolutions of the crank a, then the wavelength λ is:
Assuming that the pipe is finite and closed at the point r situated at a distance which is multiple of λ, and considering that the piston is smaller than wavelength, at r the wave compression is stopped and reflected, the reflected wave traveling back along the pipe.
Considering any flow or pipes, if:
and
then we have:
Assuming that the fluid current is produced by a piston having a simple harmonic movement, in a piston cylinder having a section of Ω square centimeters. If we have:
Then:
Where:
If T= period of a complete alternation (one revolution of the crank) then:
The effective current can be defined by the equation:
The stroke volume δ will be given by the relation:
The alternating pressures are very similar to alternating currents in electricity. In a pipe where the currents are flowing, we will have:
Considering the above formulas:
If p1 is the pressure at an arbitrary point and p2 pressure in another arbitrary point:
The effective hydromotive force will be:
In alternating current flowing through a pipe, there is friction at the surface of the pipe and also in the liquid itself. Therefore, the relation between the hydromotive force and current can be written as:
Using experiments R may be calculated from formula:
Where:
If we introduce in the formula, we get:
For pipes with a greater diameter, a greater velocity can be achieved for same value of k. The loss of power due to friction is calculated by:
Definition: Hydraulic condensers are appliances for making alterations in value of fluid currents, pressures or phases of alternating fluid currents. The apparatus usually consists of a mobile solid body, which divides the liquid column, and is fixed elastically in a middle position such that it follows the movements of the liquid column.
The principal function of hydraulic condensers is to counteract inertia effects due to moving masses.
Hydraulic Condenser Drawing | Theory |
---|---|
![]() ![]() ![]() The principal function of hydraulic condensers is to counteract inertial effects due to moving masses. The capacity C of a condenser consisting of a piston of section ω on which the liquid pressure is acting, held in a mean position by means of springs, is given by the equation:
where:
and
For a spring wire of circular section: Where
and
Therefore:
m being a constant depending on σ and G. If d is the diameter of the spring wire and the D the mean diameter of the spring. Then: so that: if we consider :: then: The above equations are used in order to calculate the springs required for a condenser of a given capacity required to work at a given maximum stress. |
{{
cite web}}
: CS1 maint: archived copy as title (
link)
![]() | This article includes a list of general
references, but it lacks sufficient corresponding
inline citations. (March 2010) |
The theory of sonics is a branch of continuum mechanics which describes the transmission of mechanical energy through vibrations. The birth of the theory of sonics [1] is the publication of the book A treatise on transmission of power by vibrations in 1918 by the Romanian scientist Gogu Constantinescu.
ONE of the fundamental problems of mechanical engineering is that of transmitting energy found in nature, after suitable transformation, to some point at which can be made available for performing useful work. The methods of transmitting power known and practised by engineers are broadly included in two classes: mechanical including hydraulic, pneumatic and wire rope methods; and electrical methods....According to the new system, energy is transmitted from one point to another, which may be at a considerable distance, by means of impressed variations of pressure or tension producing longitudinal vibrations in solid, liquid or gaseous columns. The energy is transmitted by periodic changes of pressure and volume in the longitudinal direction and may be described as wave transmission of power, or mechanical wave transmission. – Gogu Constantinescu [2] [3]
Later on the theory was expanded in electro-sonic, hydro-sonic, sonostereo-sonic and thermo-sonic. The theory was the first chapter of compressible flow applications and has stated for the first time the mathematical theory of compressible fluid, and was considered a branch of continuum mechanics. The laws discovered by Constantinescu, used in sonicity are the same with the laws used in electricity.
The book A treatise on transmission of power by vibrations has the following chapters:
George Constantinescu defined his work as follow.
If v is the velocity of which waves travel along the pipe, and n the number of the revolutions of the crank a, then the wavelength λ is:
Assuming that the pipe is finite and closed at the point r situated at a distance which is multiple of λ, and considering that the piston is smaller than wavelength, at r the wave compression is stopped and reflected, the reflected wave traveling back along the pipe.
Considering any flow or pipes, if:
and
then we have:
Assuming that the fluid current is produced by a piston having a simple harmonic movement, in a piston cylinder having a section of Ω square centimeters. If we have:
Then:
Where:
If T= period of a complete alternation (one revolution of the crank) then:
The effective current can be defined by the equation:
The stroke volume δ will be given by the relation:
The alternating pressures are very similar to alternating currents in electricity. In a pipe where the currents are flowing, we will have:
Considering the above formulas:
If p1 is the pressure at an arbitrary point and p2 pressure in another arbitrary point:
The effective hydromotive force will be:
In alternating current flowing through a pipe, there is friction at the surface of the pipe and also in the liquid itself. Therefore, the relation between the hydromotive force and current can be written as:
Using experiments R may be calculated from formula:
Where:
If we introduce in the formula, we get:
For pipes with a greater diameter, a greater velocity can be achieved for same value of k. The loss of power due to friction is calculated by:
Definition: Hydraulic condensers are appliances for making alterations in value of fluid currents, pressures or phases of alternating fluid currents. The apparatus usually consists of a mobile solid body, which divides the liquid column, and is fixed elastically in a middle position such that it follows the movements of the liquid column.
The principal function of hydraulic condensers is to counteract inertia effects due to moving masses.
Hydraulic Condenser Drawing | Theory |
---|---|
![]() ![]() ![]() The principal function of hydraulic condensers is to counteract inertial effects due to moving masses. The capacity C of a condenser consisting of a piston of section ω on which the liquid pressure is acting, held in a mean position by means of springs, is given by the equation:
where:
and
For a spring wire of circular section: Where
and
Therefore:
m being a constant depending on σ and G. If d is the diameter of the spring wire and the D the mean diameter of the spring. Then: so that: if we consider :: then: The above equations are used in order to calculate the springs required for a condenser of a given capacity required to work at a given maximum stress. |
{{
cite web}}
: CS1 maint: archived copy as title (
link)