A pressure tank or pressurizer is used in a piping system to maintain a desired pressure. Applications include buffering water pressure in homes. [1]
A pressure tank or pressurizer is 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.
In thermodynamics, enthalpy is the sum of a thermodynamic system's internal energy and the product of its pressure and volume. It is a state function 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.
A calorimeter is a device used for calorimetry, or the process of measuring the heat of chemical reactions or physical changes as well as heat capacity. Differential scanning calorimeters, isothermal micro calorimeters, titration calorimeters and accelerated rate calorimeters are among the most common types. A simple calorimeter just consists of a thermometer attached to a metal container full of water suspended above a combustion chamber. It is one of the measurement devices used in the study of thermodynamics, chemistry, and biochemistry.
Bernoulli's principle is a key concept in fluid dynamics that relates pressure, speed and height. Bernoulli's principle states that an increase in the speed of a parcel of fluid occurs simultaneously with a decrease in either the pressure or the height above a datum. The principle is named after the Swiss mathematician and physicist Daniel Bernoulli, who published it in his book Hydrodynamica in 1738. Although Bernoulli deduced that pressure decreases when the flow speed increases, it was Leonhard Euler in 1752 who derived Bernoulli's equation in its usual form.
An Otto cycle is an idealized thermodynamic cycle that describes the functioning of a typical spark ignition piston engine. It is the thermodynamic cycle most commonly found in automobile engines.
An isothermal process is a type of thermodynamic process in which the temperature T of a system remains constant: ΔT = 0. This typically occurs when a system is in contact with an outside thermal reservoir, and a change in the system occurs slowly enough to allow the system to be continuously adjusted to the temperature of the reservoir through heat exchange (see quasi-equilibrium). In contrast, an adiabatic process is where a system exchanges no heat with its surroundings (Q = 0).
In thermodynamics, an isobaric process is a type of thermodynamic process in which the pressure of the system stays constant: ΔP = 0. The heat transferred to the system does work, but also changes the internal energy (U) of the system. This article uses the physics sign convention for work, where positive work is work done by the system. Using this convention, by the first law of thermodynamics,
Hydraulic shock is a pressure surge or wave caused when a fluid in motion is forced to stop or change direction suddenly; a momentum change. It is usually observed in a liquid but gases can also be affected. This phenomenon commonly occurs when a valve closes suddenly at an end of a pipeline system and a pressure wave propagates in the pipe.
A compressor is a mechanical device that increases the pressure of a gas by reducing its volume. An air compressor is a specific type of gas compressor.
The classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself using thrust by expelling part of its mass with high velocity and can thereby move due to the conservation of momentum. It is credited to Konstantin Tsiolkovsky, who independently derived it and published it in 1903, although it had been independently derived and published by William Moore in 1810, and later published in a separate book in 1813. Robert Goddard also developed it independently in 1912, and Hermann Oberth derived it independently about 1920.
In science and engineering, hydraulic conductivity, is a property of porous materials, soils and rocks, that describes the ease with which a fluid can move through the pore space, or fracture network. It depends on the intrinsic permeability of the material, the degree of saturation, and on the density and viscosity of the fluid. Saturated hydraulic conductivity, Ksat, describes water movement through saturated media. By definition, hydraulic conductivity is the ratio of volume flux to hydraulic gradient yielding a quantitative measure of a saturated soil's ability to transmit water when subjected to a hydraulic gradient.
A thermodynamic cycle consists of linked sequences of thermodynamic processes that involve transfer of heat and work into and out of the system, while varying pressure, temperature, and other state variables within the system, and that eventually returns the system to its initial state. In the process of passing through a cycle, the working fluid (system) may convert heat from a warm source into useful work, and dispose of the remaining heat to a cold sink, thereby acting as a heat engine. Conversely, the cycle may be reversed and use work to move heat from a cold source and transfer it to a warm sink thereby acting as a heat pump. If at every point in the cycle the system is in thermodynamic equilibrium, the cycle is reversible. Whether carried out reversible or irreversibly, the net entropy change of the system is zero, as entropy is a state function.
In numerical methods, total variation diminishing (TVD) is a property of certain discretization schemes used to solve hyperbolic partial differential equations. The most notable application of this method is in computational fluid dynamics. The concept of TVD was introduced by Ami Harten.
The Navier–Stokes existence and smoothness problem concerns the mathematical properties of solutions to the Navier–Stokes equations, a system of partial differential equations that describe the motion of a fluid in space. Solutions to the Navier–Stokes equations are used in many practical applications. However, theoretical understanding of the solutions to these equations is incomplete. In particular, solutions of the Navier–Stokes equations often include turbulence, which remains one of the greatest unsolved problems in physics, despite its immense importance in science and engineering.
Lung compliance, or pulmonary compliance, is a measure of the lung's ability to stretch and expand. In clinical practice it is separated into two different measurements, static compliance and dynamic compliance. Static lung compliance is the change in volume for any given applied pressure. Dynamic lung compliance is the compliance of the lung at any given time during actual movement of air.
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.
