A pressure tank or pressurizer is a type of hydraulic accumulator used in a piping system to maintain a desired pressure. Applications include buffering water pressure in homes. [1]
A pressure tank or pressurizer is a type of hydraulic accumulator used in a piping system to maintain a desired pressure. Applications include buffering water pressure in homes. [1]
Referring to the figure on the left, a submersible water pump is installed in a well. The pressure switch turns the water pump on when it senses a pressure that is less than Plo and turns it off when it senses a pressure greater than Phi. While the pump is on, the pressure tank fills up. The pressure tank is then depleted as it supplies water in the specified pressure range to prevent "short-cycling", in which the pump tries to establish the proper pressure by rapidly cycling between Plo and Phi.
A simple pressure tank would be just a tank which held water with an air space above the water which would compress as more water entered the tank. Modern systems isolate the water from the pressurized air using a flexible rubber or plastic diaphragm or bladder, because otherwise the air will dissolve in the water and be removed from the tank by usage. Eventually there will be little or no air and the tank will become "waterlogged" causing short-cycling, and will need to be drained to restore operation. The diaphragm or bladder may itself exert a pressure on the water, but it is usually small and will be neglected in the following discussion.
Referring to the diagram on the right, a pressure tank is generally pressurized when empty with a "charging pressure" Pc, which is usually about 2 psi below the turn-on pressure Plo (Case 1). The total volume of the tank is Vt. When in use, the air in the tank will be compressed to pressure P and there will be a volume V of water in the tank (Case 2). In the following development, all pressures are gauge pressures, which are the pressures above atmospheric pressure (Pa, which is altitude dependent). The ideal gas law may be written for both cases, and the amount of air in each case is equal:
where N is the number of molecules of gas (equal in both cases), k is the Boltzmann constant and T is the temperature. Assuming that the temperature is equal for both cases, the above equations can be solved for the water pressure/volume relationship in the tank:
Tanks are generally specified by their total volume Vt and the "drawdown" (ΔV), which is the amount of water the tank will eject as the tank pressure goes from Phi to Plo, which are established by the pressure switch: [2] [3]
The reason for the charging pressure can now be seen: The larger the charging pressure, the larger the drawdown. However, a charging pressure above Plo will not allow the pump to turn on when the water pressure is below Plo, so it is kept a bit below Plo. Another important parameter is the drawdown factor (fΔV), which is the ratio of the drawdown to the total tank volume:
This factor is independent of the tank size so that the drawdown can be calculated for any tank, given its total volume, atmospheric pressure, charging pressure, and the limiting pressures established by the pressure switch.
Enthalpy is the sum of a thermodynamic system's internal energy and the product of its pressure and volume. It is a state function in thermodynamics used in many measurements in chemical, biological, and physical systems at a constant external pressure, which is conveniently provided by the large ambient atmosphere. The pressure–volume term expresses the work that was done against constant external pressure to establish the system's physical dimensions from to some final volume , i.e. to make room for it by displacing its surroundings. The pressure-volume term is very small for solids and liquids at common conditions, and fairly small for gases. Therefore, enthalpy is a stand-in for energy in chemical systems; bond, lattice, solvation, and other chemical "energies" are actually enthalpy differences. As a state function, enthalpy depends only on the final configuration of internal energy, pressure, and volume, not on the path taken to achieve it.
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Thermodynamic heat pump cycles or refrigeration cycles are the conceptual and mathematical models for heat pump, air conditioning and refrigeration systems. A heat pump is a mechanical system that transmits heat from one location at a certain temperature to another location at a higher temperature. Thus a heat pump may be thought of as a "heater" if the objective is to warm the heat sink, or a "refrigerator" or “cooler” if the objective is to cool the heat source. The operating principles in both cases are the same; energy is used to move heat from a colder place to a warmer place.
In fluid dynamics, Luke's variational principle is a Lagrangian variational description of the motion of surface waves on a fluid with a free surface, under the action of gravity. This principle is named after J.C. Luke, who published it in 1967. This variational principle is for incompressible and inviscid potential flows, and is used to derive approximate wave models like the mild-slope equation, or using the averaged Lagrangian approach for wave propagation in inhomogeneous media.
In fluid dynamics, the mild-slope equation describes the combined effects of diffraction and refraction for water waves propagating over bathymetry and due to lateral boundaries—like breakwaters and coastlines. It is an approximate model, deriving its name from being originally developed for wave propagation over mild slopes of the sea floor. The mild-slope equation is often used in coastal engineering to compute the wave-field changes near harbours and coasts.
The Thomas–Fermi (TF) model, named after Llewellyn Thomas and Enrico Fermi, is a quantum mechanical theory for the electronic structure of many-body systems developed semiclassically shortly after the introduction of the Schrödinger equation. It stands separate from wave function theory as being formulated in terms of the electronic density alone and as such is viewed as a precursor to modern density functional theory. The Thomas–Fermi model is correct only in the limit of an infinite nuclear charge. Using the approximation for realistic systems yields poor quantitative predictions, even failing to reproduce some general features of the density such as shell structure in atoms and Friedel oscillations in solids. It has, however, found modern applications in many fields through the ability to extract qualitative trends analytically and with the ease at which the model can be solved. The kinetic energy expression of Thomas–Fermi theory is also used as a component in more sophisticated density approximation to the kinetic energy within modern orbital-free density functional theory.
ΔP is a mathematical term symbolizing a change (Δ) in pressure (P).
A non-expanding horizon (NEH) is an enclosed null surface whose intrinsic structure is preserved. An NEH is the geometric prototype of an isolated horizon which describes a black hole in equilibrium with its exterior from the quasilocal perspective. It is based on the concept and geometry of NEHs that the two quasilocal definitions of black holes, weakly isolated horizons and isolated horizons, are developed.
