http://mihd।net/1yof2v
Hydraulics is a topic of science and engineering subject dealing with the mechanical properties of liquids. Hydraulics is part of the more general discipline of fluid power. Fluid mechanicsengineering uses of fluid properties. Hydraulic topics range through most science and engineering disciplines, and cover concepts such as pipe flow, dam design, fluid control circuitry, pumps, turbines, hydropower, computational fluid dynamics, flow measurement, river channel behavior and erosion. provides the theoretical foundation for hydraulics, which focuses on the
The word "hydraulics" originates from the Greek word ὑδραυλικός (hydraulikos) which in turn originates from ὕδραυλος meaning water organ which in turn comes from ὕδρω (water) and αὐλός (pipe).
The earliest masters of this art were Ctesibius (flourished c. 270 BC) and Hero of Alexandria (c. 10–70 AD) in the Greek-Hellenized West, while ancient China had those such as Du Shi (circa 31 AD), Zhang Heng (78 - 139 AD), Ma Jun (200 - 265 AD), and Su Song (1020 - 1101 AD). The ancient engineers focused on sacral and novelty uses of hydraulics, rather than practical applications. Ancient Sinhalese used hydraulics in many applications, in the Ancient kingdoms of Anuradhapura, Polonnaruwa etc. The discovery of the principle of the valve tower, or valve pit, for regulating the escape of water is credited to Sinhalese ingenuity more than 2,000 years ago. By the first century A.D, several large-scale irrigation works had been completed. Macro- and micro-hydraulics to provide for domestic horticultural and agricultural needs, surface drainage and erosion control, ornamental and recreational water courses and retaining structures and also cooling systems were in place in Sigiriya, Sri Lanka.
In 1690 Benedetto Castelli (1578–1643), a student of Galileo Galilei, published the book Della Misura dell'Acque Correnti or "On the Measurement of Running Waters," one of the foundations of modern hydrodynamics. He served as a chief consultant to the Pope on hydraulic projects, i.e., management of rivers in the Papal States, beginning in 1626.[1]
Blaise Pascal's (1623–1662) study of fluid hydrodynamics and hydrostatics centered on the principles of hydraulic fluids. His inventions include the hydraulic press, which multiplied a smaller force acting on a smaller area into the application of a larger force totaled over a larger area, transmitted through the same pressure (or same change of pressure) at both locations. Pascal's law or principle states that for an incompressible fluid at rest, the difference in pressure is proportional to the difference in height and this difference remains the same whether or not the overall pressure of the fluid is changed by applying an external force. This implies that by increasing the pressure at any point in a confined fluid, there is an equal increase at every other point in the container, i.e., any change in pressure applied at any point of the fluid is transmitted undiminished throughout the fluids.
A hydraulic/hydrostatic drive system is a drive, or transmission system, that makes use of a hydraulic fluid under pressure to drive a machinery. Such a system basically consists of a hydraulic pump, driven by an electric motor, a combustion engine or maybe a windmill, and a hydraulic motor or hydraulic cylinder to drive the machinery. Between pump and motor/cylinder, valves, filters, piping etc guide, maintain and control the drive system. Hydrostatic means that the energy comes from the flow and the pressure, but not from the kinetic energy of the flow.
For further details go to http://galileo.rice.edu/sci/instruments/pump.html
Suppose we have a number of energy levels, labelled by index i, each level having energy εi and containing a total of ni particles. Suppose each level contains gi distinct sublevels, all of which have the same energy, and which are distinguishable. For example, two particles may have different momenta, in which case they are distinguishable from each other, yet they can still have the same energy. The value of gi associated with level i is called the "degeneracy" of that energy level. Any number of bosons can occupy the same sublevel.
Let w(n,g) be the number of ways of distributing n particles among the g sublevels of an energy level. There is only one way of distributing n particles with one sublevel, therefore w(n,1) = 1. It's easy to see that there are n + 1 ways of distributing n particles in two sublevels which we will write as:
With a little thought it can be seen that the number of ways of distributing n particles in three sublevels is w(n,3) = w(n,2) + w(n−1,2) + ... + w(0,2) so that
where we have used the following theorem involving binomial coefficients:
Continuing this process, we can see that w(n,g) is just a binomial coefficient
The number of ways that a set of occupation numbers ni can be realized is the product of the ways that each individual energy level can be populated:
where the approximation assumes that gi > > 1. Following the same procedure used in deriving the Maxwell–Boltzmann statistics, we wish to find the set of ni for which W is maximised, subject to the constraint that there be a fixed number of particles, and a fixed energy. The maxima of W and ln(W) occur at the value of Ni and, since it is easier to accomplish mathematically, we will maximise the latter function instead. We constrain our solution using Lagrange multipliers forming the function:
Using the gi > > 1 approximation and using Stirling's approximation for the factorials 
gives:
Taking the derivative with respect to ni, and setting the result to zero and solving for ni yields the Bose–Einstein population numbers:
It can be shown thermodynamically that β = 1/kT where k is Boltzmann's constant and T is the temperature, and that α = -μ/kT where μ is the chemical potential, so that finally:
Note that the above formula is sometimes written:
where z = exp(μ / kT) is the absolute activity.
