Compressible flow is the branch of fluid mechanics that deals with flows having significant changes in fluid density. Gases display such behaviour. While all flows are compressible, flows are treated as being incompressible when the Mach number is less than 0.3. The study of compressible flow is relevant to high-speed aircraft, jet engines, rocket motors, high-speed entry into a planetary atmosphere, gas pipelines, commercial applications such as abrasive blasting, many other fields; the study of gas dynamics is associated with the flight of modern high-speed aircraft and atmospheric reentry of space-exploration vehicles. At the beginning of the 19th century, investigation into the behaviour of fired bullets led to improvement in the accuracy and capabilities of guns and artillery; as the century progressed, inventors such as Gustaf de Laval advanced the field, while researchers such as Ernst Mach sought to understand the physical phenomenon involved through experimentation. At the beginning of the 20th century, the focus of gas dynamics research shifted to what would become the aerospace industry.
Ludwig Prandtl and his students proposed important concepts ranging from the boundary layer to supersonic shock waves, supersonic wind tunnels, supersonic nozzle design. Theodore von Kármán, a student of Prandtl, continued to improve the understanding of supersonic flow. Other notable figures contributed to the principles considered fundamental to the study of modern gas dynamics. Many others contributed to this field. Accompanying the improved conceptual understanding of gas dynamics in the early 20th century was a public misconception that there existed a barrier to the attainable speed of aircraft referred to as the "sound barrier." In truth, the barrier to supersonic flight was a technological one, although it was a stubborn barrier to overcome. Amongst other factors, conventional aerofoils saw a dramatic increase in drag coefficient when the flow approached the speed of sound. Overcoming the larger drag proved difficult with contemporary designs, thus the perception of a sound barrier. However, aircraft design progressed sufficiently to produce the Bell X-1.
Piloted by Chuck Yeager, the X-1 achieved supersonic speed in October 1947. Two parallel paths of research have been followed in order to further gas dynamics knowledge. Experimental gas dynamics undertakes wind tunnel model experiments and experiments in shock tubes and ballistic ranges with the use of optical techniques to document the findings. Theoretical gas dynamics considers the equations of motion applied to a variable-density gas, their solutions. Much of basic gas dynamics is analytical, but in the modern era Computational fluid dynamics applies computing power to solve the otherwise-intractable nonlinear partial differential equations of compressible flow for specific geometries and flow characteristics. There are several important assumptions involved in the underlying theory of compressible flow. All fluids are composed of molecules, but tracking a huge number of individual molecules in a flow is unnecessary. Instead, the continuum assumption allows us to consider a flowing gas as a continuous substance except at low densities.
This assumption provides a huge simplification, accurate for most gas-dynamic problems. Only in the low-density realm of rarefied gas dynamics does the motion of individual molecules become important. A related assumption is the no-slip condition where the flow velocity at a solid surface is presumed equal to the velocity of the surface itself, a direct consequence of assuming continuum flow; the no-slip condition implies that the flow is viscous, as a result a boundary layer forms on bodies traveling through the air at high speeds, much as it does in low-speed flow. Most problems in incompressible flow involve only two unknowns: pressure and velocity, which are found by solving the two equations that describe conservation of mass and of linear momentum, with the fluid density presumed constant. In compressible flow, the gas density and temperature become variables; this requires two more equations in order to solve compressible-flow problems: an equation of state for the gas and a conservation of energy equation.
For the majority of gas-dynamic problems, the simple Ideal gas law is the appropriate state equation. Fluid dynamics problems have two overall types of references frames, called Eulerian; the Lagrangian approach follows a fluid mass of fixed identity. The Eulerian reference frame, in contrast, does not move with the fluid. Rather it is a fixed control volume that fluid flows through; the Eulerian frame is most useful in a majority of compressible flow problems, but requires that the equations of motion be written in a compatible format. Although space is known to have 3 dimensions, an important simplification can be had in describing gas dynamics mathematically if only one spatial dimension is of primary importance, hence 1-dimensional flow is assumed; this works well in duct and diffuser flows where the flow properties change in the flow direction rather than perpendicular to the flow. However, an important class of compressible flows, including the external flow over bodies traveling at high speed, requires at least a 2-dimensional treatment.
When all 3 spatial dimensions and the time dimension as well are important, we reso
Enthalpy, a property of a thermodynamic system, is equal to the system's internal energy plus the product of its pressure and volume. In a system enclosed so as to prevent matter transfer, for processes at constant pressure, the heat absorbed or released equals the change in enthalpy; the unit of measurement for enthalpy in the International System of Units is the joule. Other historical conventional units still in use include the calorie. Enthalpy comprises a system's internal energy, the energy required to create the system, plus the amount of work required to make room for it by displacing its environment and establishing its volume and pressure. Enthalpy is defined as a state function that depends only on the prevailing equilibrium state identified by the system's internal energy and volume, it is an extensive quantity. Enthalpy is the preferred expression of system energy changes in many chemical and physical measurements at constant pressure, because it simplifies the description of energy transfer.
In a system enclosed so as to prevent matter transfer, at constant pressure, the enthalpy change equals the energy transferred from the environment through heat transfer or work other than expansion work. The total enthalpy, H, of a system cannot be measured directly; the same situation exists in classical mechanics: only a change or difference in energy carries physical meaning. Enthalpy itself is a thermodynamic potential, so in order to measure the enthalpy of a system, we must refer to a defined reference point; the ΔH is a positive change in endothermic reactions, negative in heat-releasing exothermic processes. For processes under constant pressure, ΔH is equal to the change in the internal energy of the system, plus the pressure-volume work p ΔV done by the system on its surroundings; this means that the change in enthalpy under such conditions is the heat absorbed or released by the system through a chemical reaction or by external heat transfer. Enthalpies for chemical substances at constant pressure refer to standard state: most 1 bar pressure.
Standard state does not speaking, specify a temperature, but expressions for enthalpy reference the standard heat of formation at 25 °C. Enthalpy of ideal gases and incompressible solids and liquids does not depend on pressure, unlike entropy and Gibbs energy. Real materials at common temperatures and pressures closely approximate this behavior, which simplifies enthalpy calculation and use in practical designs and analyses; the word enthalpy was coined late, in the early 20th century, in analogy with the 19th-century terms energy and entropy. Where energy uses the root of the Greek word ἔργον "work" to express the idea of "work-content" and where entropy uses the Greek word τροπή "transformation" to express the idea of "transformation-content", so by analogy, enthalpy uses the root of the Greek word θάλπος "warmth, heat" to express the idea of "heat-content"; the term does in fact stand in for the older term "heat content", a term, now deprecated as misleading, as dH refers to the amount of heat absorbed in a process at constant pressure only, but not in the general case.
Josiah Willard Gibbs used the term "a heat function for constant pressure" for clarity. Introduction of the concept of "heat content" H is associated with Benoît Paul Émile Clapeyron and Rudolf Clausius; the term enthalpy first appeared in print in 1909. It is attributed to Heike Kamerlingh Onnes, who most introduced it orally the year before, at the first meeting of the Institute of Refrigeration in Paris, it gained currency only in the 1920s, notably with the Mollier Steam Tables and Diagrams, published in 1927. Until the 1920s, the symbol H was used, somewhat inconsistently, for "heat" in general; the definition of H as limited to enthalpy or "heat content at constant pressure" was formally proposed by Alfred W. Porter in 1922; the enthalpy of a thermodynamic system is defined as H = U + p V, where H is enthalpy U is the internal energy of the system p is pressure V is the volume of the systemEnthalpy is an extensive property. This means, it is convenient to introduce the specific enthalpy h = H m, where m is the mass of the system, or the molar enthalpy H m = H n, where n is the number of moles.
For inhomogeneous systems the enthalpy is the sum of the enthalpies of the composing subsystems: H = ∑ k H k, where H is the total enthalpy of all the subsystems k refers to the various subsystems H k refers to the enthalpy of each subsystem ∑ k
SpaceAge Control is a design and service company focused on 3D displacement sensing and measurement. The company has supplied precision displacement sensors to industries worldwide since 1969. During its history, the company has created a number of displacement sensing innovations: originator of the miniature and subminiature string potentiometerv smallest cable-type displacement sensor in the world DirectConnect sensor installation eliminates backlash error AccuTrak threaded drum ensures repeatability RoundAbout cable exit allows dynamic 3D tracking and reduces installation time to seconds patented universal base offers unparalleled mounting flexibility transducer-mounted idlers give 2D motion-tracking flexibility man-rated, space-qualified, redundant sensors for the ultimate in reliability originators of the first 2D and 3D cable-actuated displacement sensors SpaceAge Control was established in 1968 to design and manufacture pilot protection devices in support of space-based and high-performance test aircraft programs.
In 1970, the company was awarded a NASA contract to produce precision, small-format position transducers for aircraft flight control testing. The successful completion of this contract led to the development and production of a complete line of innovative, small-size position transducers. In 1974, the company was tasked with producing a multi-dimensional "swivel head" air data probe to enhance total and static pressure accuracy at the high angles of attack associated with rotary wing aircraft; the resulting product, the 100510 air data boom, is used for flight test air data sensing requirements to include STOL, VSTOL, rotary wing, business jet, military transport, general aviation aircraft. Through the 1970s, 1980s, 1990s all U. S. Canadian, European aerospace companies have used the company's air data products and position transducers in their research and test activities; these products were designed and manufactured to custom specifications. In 1989, the company began its focus on unmanned aerial vehicles with the development and introduction of the 100400 miniature air data boom.
That product use led to the adoption of SpaceAge Control air data products on a broad range of unmanned aircraft to include aerial targets, autonomous vehicles, experimental vehicles. In 1989, a single auto racing team began using these position transducers to monitor throttle movement and suspension travel; this use resulted in the adoption of the products in automotive test and measurement projects including anthropomorphic dummy instrumentation, impact testing, control verification. OEM displacement sensors MMI sensors CMM sensors String Potentiometer and String Encoder Engineering Guide Google Finance Entry for Company SpaceAge Control, Inc. website DSPM Industria - webpage, Italian Distributor
In fluid dynamics, a stagnation point is a point in a flow field where the local velocity of the fluid is zero. Stagnation points exist at the surface of objects in the flow field, where the fluid is brought to rest by the object; the Bernoulli equation shows that the static pressure is highest when the velocity is zero and hence static pressure is at its maximum value at stagnation points. This static pressure is called the stagnation pressure; the Bernoulli equation applicable to incompressible flow shows that the stagnation pressure is equal to the dynamic pressure plus static pressure. Total pressure is equal to dynamic pressure plus static pressure so, in incompressible flows, stagnation pressure is equal to total pressure; this information can be used to show that the pressure coefficient C p at a stagnation point is unity: C p = p − p ∞ q ∞ where: C p is pressure coefficient p is static pressure at the point at which pressure coefficient is being evaluated p ∞ is static pressure at points remote from the body q ∞ is dynamic pressure at points remote from the body Stagnation pressure minus freestream static pressure is equal to freestream dynamic pressure.
On a streamlined body immersed in a potential flow, there are two stagnation points—one near the leading edge and one near the trailing edge. On a body with a sharp point such as the trailing edge of a wing, the Kutta condition specifies that a stagnation point is located at that point; the streamline at a stagnation point is perpendicular to the surface of the body. Stagnation point flow
A hydraulic ram, or hydram, is a cyclic water pump powered by hydropower. It takes in water at one "hydraulic head" and flow rate, outputs water at a higher hydraulic head and lower flow rate; the device uses the water hammer effect to develop pressure that allows a portion of the input water that powers the pump to be lifted to a point higher than where the water started. The hydraulic ram is sometimes used in remote areas, where there is both a source of low-head hydropower and a need for pumping water to a destination higher in elevation than the source. In this situation, the ram is useful, since it requires no outside source of power other than the kinetic energy of flowing water. In 1772, John Whitehurst of Cheshire, United Kingdom, invented a manually controlled precursor of the hydraulic ram called the "pulsation engine" and installed the first one at Oulton, Cheshire to raise water to a height of 4.9 metres. In 1783, he installed another in Ireland, he did not patent it, details are obscure, but it is known to have had an air vessel.
The first self-acting ram pump was invented by the Frenchman Joseph Michel Montgolfier in 1796 for raising water in his paper mill at Voiron. His friend Matthew Boulton took out a British patent on his behalf in 1797; the sons of Montgolfier obtained a British patent for an improved version in 1816, this was acquired, together with Whitehurst's design, in 1820 by Josiah Easton, a Somerset-born engineer who had just moved to London. Easton's firm, inherited by his son James, grew during the nineteenth century to become one of the more important engineering manufacturers in the United Kingdom, with a large works at Erith, Kent, they sewerage systems worldwide, as well as land drainage projects. Eastons had a good business supplying rams for water supply purposes to large country houses and village communities; some of their installations still survived as of 2004, one such example being at the hamlet of Toller Whelme, in Dorset. Until about 1958 when the mains water arrived, the hamlet of East Dundry just south of Bristol had three working rams – their noisy "thump" every minute or so resonated through the valley night and day: these rams served farms that needed much water for their dairy herds.
The firm closed in 1909. In 1929, it was acquired by Green & Carter of Winchester, who were engaged in the manufacturing and installation of Vulcan and Vacher Rams; the first US patent was issued to Joseph Cerneau and Stephen S. Hallet in 1809. US interest in hydraulic rams picked up around 1840, as further patents were issued and domestic companies started offering rams for sale. Toward the end of the 19th century, interest waned as electricity and electric pumps became available. By the end of the twentieth century interest in hydraulic rams has revived, due to the needs of sustainable technology in developing countries, energy conservation in developed ones. A good example is AID Foundation International in the Philippines, who won an Ashden Award for their work developing ram pumps that could be maintained for use in remote villages; the hydraulic ram principle has been used in some proposals for exploiting wave power, one of, discussed as long ago as 1931 by Hanns Günther in his book In hundert Jahren.
Some ram designs in the UK called compound rams were designed to pump treated water using an untreated drive water source, which overcomes some of the problems of having drinking water sourced from an open stream. In 1996 an English engineer, Frederick Philip Selwyn, patented a ‘fluid pressure amplifier’ which differed in many ways to the contemporary ram technology by the development of a venturi effect waste valve. Known as the Papa pump, this utilises the low pressure generated by high velocity water flow around a curve-shaped elastomeric valve to allow a valve design that enables rapid closure and with a small cross sectional area and low weight; the venturi valve is configured as a ring section positioned around the supply inlet of the pump with the delivery outlet of the pump being directly in line. The design allowed the pump structure to be concentric and therefore inherently strong and upon closure of the valve, permits efficient water delivery by acting in line with the supply via a second smaller venturi effect delivery non return valve.
The elastomeric material and operation of these valves allows them to self-return without weight or spring assistance. A pressure vessel installed on a tee connected to the delivery port of the pump provides the pulsed flow accumulation means; this unique technology and design reduced the weight, manufacturing cost and number of components required - as well as provided an overall improvement in efficiency. Additional patents granted to Selwyn have since been developed by UK companies Papa Ltd and Water Powered Technologies Ltd of Bude, further enhancing the technology to include a composite material injection-moulded pump allowing for low cost mass production whilst maintaining high strength, low weight and high performance only attainable with metal units. Other novel developments include an automatic regulator valve which can be installed to the pumps to allow the maximum utilisation of water supply from low or seasonally variable water sources without the need to manually adjust the pumps - as well as much larger pump versions with one metre diameter inlets for large river, marine tidal and flood applications.
Systems have been developed and utilised for rainwater harvesting, water treatment and other water utility
A pitot tube known as pitot probe, is a flow measurement device used to measure fluid flow velocity. The pitot tube was invented by the French engineer Henri Pitot in the early 18th century and was modified to its modern form in the mid-19th century by French scientist Henry Darcy, it is used to determine the airspeed of an aircraft, water speed of a boat, to measure liquid and gas flow velocities in certain industrial applications. The basic pitot tube consists of a tube pointing directly into the fluid flow; as this tube contains fluid, a pressure can be measured. This pressure is the stagnation pressure of the fluid known as the total pressure or the pitot pressure; the measured stagnation pressure cannot itself be used to determine the fluid flow velocity. However, Bernoulli's equation states: Stagnation pressure = static pressure + dynamic pressureWhich can be written p t = p s +. Solving that for flow velocity gives u = 2 ρ, where u is the flow velocity. NOTE: The above equation applies only to fluids that can be treated as incompressible.
Liquids are treated as incompressible under all conditions. Gases under certain conditions can be approximated as incompressible. See Compressibility; the dynamic pressure is the difference between the stagnation pressure and the static pressure. The dynamic pressure is determined using a diaphragm inside an enclosed container. If the air on one side of the diaphragm is at the static pressure, the other at the stagnation pressure the deflection of the diaphragm is proportional to the dynamic pressure. In aircraft, the static pressure is measured using the static ports on the side of the fuselage; the dynamic pressure measured can be used to determine the indicated airspeed of the aircraft. The diaphragm arrangement described above is contained within the airspeed indicator, which converts the dynamic pressure to an airspeed reading by means of mechanical levers. Instead of separate pitot and static ports, a pitot-static tube may be employed, which has a second tube coaxial with the pitot tube with holes on the sides, outside the direct airflow, to measure the static pressure.
If a liquid column manometer is used to measure the pressure difference Δ p ≡ p t − p s, Δ h = Δ p ρ l g, where Δ h is the height difference of the columns. Therefore, u = 2 Δ h ρ l g ρ. A pitot-static system is a system of pressure-sensitive instruments, most used in aviation to determine an aircraft's airspeed, Mach number and altitude trend. A pitot-static system consists of a pitot tube, a static port, the pitot-static instruments. Errors in pitot-static system readings can be dangerous as the information obtained from the pitot static system, such as airspeed, is safety-critical. Several commercial airline incidents and accidents have been traced to a failure of the pitot-static system. Examples include Austral Líneas Aéreas Flight 2553, Northwest Airlines Flight 6231, Birgenair Flight 301 and one of the two X-31s; the French air safety authority BEA said that pitot tube icing was a contributing factor in the crash of Air France Flight 447 into the Atlantic Ocean. In 2008 Air Caraïbes reported two incidents of pitot tube icing malfunctions on its A330s.
Birgenair Flight 301 had a fatal pitot tube failure which investigators suspected was due to insects creating a nest inside the pitot tube. Aeroperú Flight 603 had a pitot-static system failure due to the cleaning crew leaving the static port blocked with tape. In industry, the flow velocities being measured are those flowing in ducts and tubing where measurements by an anemometer would be difficult to obtain. In these kinds of measurements, the most practical instrument to use is the pitot tube; the pitot tube can be inserted through a small hole in the duct with the pitot connected to a U-tube water gauge or some other differential pressure gauge for determining the flow velocity inside the ducted wind tunnel. One use of this technique is to determine the volume of air, being delivered to a conditioned space; the fluid flow rate in a duct can be estimated from
In thermodynamics, an isentropic process is an idealized thermodynamic process, both adiabatic and reversible. The work transfers of the system are frictionless, there is no transfer of heat or matter; such an idealized process is useful in engineering as a model of and basis of comparison for real processes. The word "isentropic" is though not customarily, interpreted in another way, reading it as if its meaning were deducible from its etymology; this customarily used definition. In this occasional reading, it means a process. For example, this could occur in a system where the work done on the system includes friction internal to the system, heat is withdrawn from the system in just the right amount to compensate for the internal friction, so as to leave the entropy unchanged; the second law of thermodynamics states that T s u r r d S ≥ δ Q, where δ Q is the amount of energy the system gains by heating, T s u r r is the temperature of the surroundings, d S is the change in entropy. The equal sign refers to a reversible process, an imagined idealized theoretical limit, never occurring in physical reality, with equal temperatures of system and surroundings.
For an isentropic process, which by definition is reversible, there is no transfer of energy as heat because the process is adiabatic, δQ = 0. In an irreversible process of transfer of energy as work, entropy is produced within the system. For reversible processes, an isentropic transformation is carried out by thermally "insulating" the system from its surroundings. Temperature is the thermodynamic conjugate variable to entropy, thus the conjugate process would be an isothermal process, in which the system is thermally "connected" to a constant-temperature heat bath; the entropy of a given mass does not change during a process, internally reversible and adiabatic. A process during which the entropy remains constant is called an isentropic process, written Δ s = 0 or s 1 = s 2; some examples of theoretically isentropic thermodynamic devices are pumps, gas compressors, turbines and diffusers. Most steady-flow devices operate under adiabatic conditions, the ideal process for these devices is the isentropic process.
The parameter that describes how efficiently a device approximates a corresponding isentropic device is called isentropic or adiabatic efficiency. Isentropic efficiency of turbines: η t = actual turbine work isentropic turbine work = W a W s ≅ h 1 − h 2 a h 1 − h 2 s. Isentropic efficiency of compressors: η c = isentropic compressor work actual compressor work = W s W a ≅ h 2 s − h 1 h 2 a − h 1. Isentropic efficiency of nozzles: η n = actual KE at nozzle exit isentropic KE at nozzle exit = V 2 a 2 V 2 s 2 ≅ h 1 − h 2 a h 1 − h 2 s. For all the above equations: h 1 is the specific enthalpy at the entrance state, h 2 a is the specific enthalpy at the exit state for the actual process, h 2 s is the specific enthalpy at the exit state for the isentropic process. Note: The isentropic assumptions are only applicable with ideal cycles. Real cycles have inherent losses due to compressor and turbine inefficiencies and the second law of thermodynamics. Real systems are not isentropic, but isentropic behavior is an adequate approximation for many calculation purposes.
In fluid dynamics, an isentropic flow is a fluid flow, both adiabatic and reversible. That is, no he