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53-491: The mountain pass acts as a venturi effect to air moving between ocean and desert, increasing wind speed. Wind development in the Tehachapi Pass began in the early 1980s by James Dehlsen and Zond Corporation . The first set of wind turbines installed were of American-made Storm Master brand, however they proved troublesome and eventually had to be replaced. Dehlsen turned to Danish-built machines later, which now make up

106-494: A variable void fraction which depends on how the material is agitated or poured. It might be loose or compact, with more or less air space depending on handling. In practice, the void fraction is not necessarily air, or even gaseous. In the case of sand, it could be water, which can be advantageous for measurement as the void fraction for sand saturated in water—once any air bubbles are thoroughly driven out—is potentially more consistent than dry sand measured with an air void. In

159-566: A Venturi, the expansion and compression of the fluids cause the pressure inside the Venturi to change. This principle can be used in metrology for gauges calibrated for differential pressures. This type of pressure measurement may be more convenient, for example, to measure fuel or combustion pressures in jet or rocket engines. The first large-scale Venturi meters to measure liquid flows were developed by Clemens Herschel who used them to measure small and large flows of water and wastewater beginning at

212-475: A constricted section (or choke) of a pipe. The Venturi effect is named after its discoverer, the 18th-century Italian physicist Giovanni Battista Venturi . The effect has various engineering applications, as the reduction in pressure inside the constriction can be used both for measuring the fluid flow and for moving other fluids (e.g. in a vacuum ejector ). In inviscid fluid dynamics , an incompressible fluid's velocity must increase as it passes through

265-494: A constriction in accord with the principle of mass continuity , while its static pressure must decrease in accord with the principle of conservation of mechanical energy ( Bernoulli's principle ) or according to the Euler equations . Thus, any gain in kinetic energy a fluid may attain by its increased velocity through a constriction is balanced by a drop in pressure because of its loss in potential energy . By measuring pressure,

318-448: A further decrease in the downstream pressure environment will not lead to an increase in velocity, unless the fluid is compressed. The mass flow rate for a compressible fluid will increase with increased upstream pressure, which will increase the density of the fluid through the constriction (though the velocity will remain constant). This is the principle of operation of a de Laval nozzle . Increasing source temperature will also increase

371-533: A liquid with a gas. If a pump forces the liquid through a tube connected to a system consisting of a Venturi to increase the liquid speed (the diameter decreases), a short piece of tube with a small hole in it, and last a Venturi that decreases speed (so the pipe gets wider again), the gas will be sucked in through the small hole because of changes in pressure. At the end of the system, a mixture of liquid and gas will appear. See aspirator and pressure head for discussion of this type of siphon . As fluid flows through

424-942: A solution sums to density of the solution, ρ = ∑ i ρ i . {\displaystyle \rho =\sum _{i}\rho _{i}.} Expressed as a function of the densities of pure components of the mixture and their volume participation , it allows the determination of excess molar volumes : ρ = ∑ i ρ i V i V = ∑ i ρ i φ i = ∑ i ρ i V i ∑ i V i + ∑ i V E i , {\displaystyle \rho =\sum _{i}\rho _{i}{\frac {V_{i}}{V}}\,=\sum _{i}\rho _{i}\varphi _{i}=\sum _{i}\rho _{i}{\frac {V_{i}}{\sum _{i}V_{i}+\sum _{i}{V^{E}}_{i}}},} provided that there

477-455: A substance does not increase its density; rather it increases its mass. Other conceptually comparable quantities or ratios include specific density , relative density (specific gravity) , and specific weight . The understanding that different materials have different densities, and of a relationship between density, floating, and sinking must date to prehistoric times. Much later it was put in writing. Aristotle , for example, wrote: There

530-399: A temperature increase on the order of thousands of degrees Celsius . In contrast, the density of gases is strongly affected by pressure. The density of an ideal gas is ρ = M P R T , {\displaystyle \rho ={\frac {MP}{RT}},} where M is the molar mass , P is the pressure, R is the universal gas constant , and T

583-411: Is mass divided by volume . As there are many units of mass and volume covering many different magnitudes there are a large number of units for mass density in use. The SI unit of kilogram per cubic metre (kg/m ) and the cgs unit of gram per cubic centimetre (g/cm ) are probably the most commonly used units for density. One g/cm is equal to 1000 kg/m . One cubic centimetre (abbreviation cc)

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636-486: Is equal to one millilitre. In industry, other larger or smaller units of mass and or volume are often more practical and US customary units may be used. See below for a list of some of the most common units of density. The litre and tonne are not part of the SI, but are acceptable for use with it, leading to the following units: Densities using the following metric units all have exactly the same numerical value, one thousandth of

689-419: Is given by p 1 − p 2 = ρ 2 ( v 2 2 − v 1 2 ) , {\displaystyle p_{1}-p_{2}={\frac {\rho }{2}}(v_{2}^{2}-v_{1}^{2}),} where ρ {\displaystyle \rho } is the density of the fluid, v 1 {\displaystyle v_{1}}

742-403: Is necessary to have an understanding of the type of density being measured as well as the type of material in question. The density at all points of a homogeneous object equals its total mass divided by its total volume. The mass is normally measured with a scale or balance ; the volume may be measured directly (from the geometry of the object) or by the displacement of a fluid. To determine

795-445: Is not tolerable and where maximum accuracy is needed in case of highly viscous liquids. Venturi tubes are more expensive to construct than simple orifice plates , and both function on the same basic principle. However, for any given differential pressure, orifice plates cause significantly more permanent energy loss. Both Venturi tubes and orifice plates are used in industrial applications and in scientific laboratories for measuring

848-453: Is small. The compressibility for a typical liquid or solid is 10   bar (1 bar = 0.1 MPa) and a typical thermal expansivity is 10   K . This roughly translates into needing around ten thousand times atmospheric pressure to reduce the volume of a substance by one percent. (Although the pressures needed may be around a thousand times smaller for sandy soil and some clays.) A one percent expansion of volume typically requires

901-488: Is so great a difference in density between salt and fresh water that vessels laden with cargoes of the same weight almost sink in rivers, but ride quite easily at sea and are quite seaworthy. And an ignorance of this has sometimes cost people dear who load their ships in rivers. The following is a proof that the density of a fluid is greater when a substance is mixed with it. If you make water very salt by mixing salt in with it, eggs will float on it. ... If there were any truth in

954-428: Is so much denser than air that the buoyancy effect is commonly neglected (less than one part in one thousand). Mass change upon displacing one void material with another while maintaining constant volume can be used to estimate the void fraction, if the difference in density of the two voids materials is reliably known. In general, density can be changed by changing either the pressure or the temperature . Increasing

1007-609: Is the absolute temperature . This means that the density of an ideal gas can be doubled by doubling the pressure, or by halving the absolute temperature. In the case of volumic thermal expansion at constant pressure and small intervals of temperature the temperature dependence of density is ρ = ρ T 0 1 + α ⋅ Δ T , {\displaystyle \rho ={\frac {\rho _{T_{0}}}{1+\alpha \cdot \Delta T}},} where ρ T 0 {\displaystyle \rho _{T_{0}}}

1060-415: Is the (slower) fluid velocity where the pipe is wider, and v 2 {\displaystyle v_{2}} is the (faster) fluid velocity where the pipe is narrower (as seen in the figure). The limiting case of the Venturi effect is when a fluid reaches the state of choked flow , where the fluid velocity approaches the local speed of sound . When a fluid system is in a state of choked flow,

1113-418: Is the densest known element at standard conditions for temperature and pressure . To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity " relative density " or " specific gravity ", i.e. the ratio of the density of the material to that of a standard material, usually water. Thus a relative density less than one relative to water means that

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1166-487: Is the density at a reference temperature, α {\displaystyle \alpha } is the thermal expansion coefficient of the material at temperatures close to T 0 {\displaystyle T_{0}} . The density of a solution is the sum of mass (massic) concentrations of the components of that solution. Mass (massic) concentration of each given component ρ i {\displaystyle \rho _{i}} in

1219-591: Is the density, m is the mass, and V is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume , although this is scientifically inaccurate – this quantity is more specifically called specific weight . For a pure substance the density has the same numerical value as its mass concentration . Different materials usually have different densities, and density may be relevant to buoyancy , purity and packaging . Osmium

1272-537: The displacement of the water. Upon this discovery, he leapt from his bath and ran naked through the streets shouting, "Eureka! Eureka!" ( Ancient Greek : Εύρηκα! , lit.   'I have found it'). As a result, the term eureka entered common parlance and is used today to indicate a moment of enlightenment. The story first appeared in written form in Vitruvius ' books of architecture , two centuries after it supposedly took place. Some scholars have doubted

1325-1128: The square root . Note that pressure-, temperature-, and mass-compensation is required for every flow, regardless of the end units or dimensions. Also we see the relations: k Δ P max = 1 ρ ⊖ Q max 2 = ρ ⊖ m ˙ max 2 = C ⊖ 2 ρ ⊖ n ˙ max 2 = C ⊖ M ⊖ n ˙ max 2 . {\displaystyle {\begin{aligned}{\frac {k}{\Delta P_{\max }}}&={\frac {1}{\rho ^{\ominus }Q_{\max }^{2}}}\\&={\frac {\rho ^{\ominus }}{{\dot {m}}_{\max }^{2}}}\\&={\frac {{C^{\ominus }}^{2}}{\rho ^{\ominus }{\dot {n}}_{\max }^{2}}}={\frac {C^{\ominus }}{M^{\ominus }{\dot {n}}_{\max }^{2}}}.\end{aligned}}} The Venturi effect may be observed or used in

1378-659: The Tehachapi region, which is triple the size of any existing U.S. wind farm. Other well-known wind turbine locations in California include the adjacent Alta Wind Energy Center , the Altamont Pass Wind Farm and the San Gorgonio Pass Wind Farm , near Palm Springs . Venturi effect The Venturi effect is the reduction in fluid pressure that results when a moving fluid speeds up as it flows through

1431-431: The accuracy of this tale, saying among other things that the method would have required precise measurements that would have been difficult to make at the time. Nevertheless, in 1586, Galileo Galilei , in one of his first experiments, made a possible reconstruction of how the experiment could have been performed with ancient Greek resources From the equation for density ( ρ = m / V ), mass density has any unit that

1484-404: The body then can be expressed as m = ∫ V ρ ( r → ) d V . {\displaystyle m=\int _{V}\rho ({\vec {r}})\,dV.} In practice, bulk materials such as sugar, sand, or snow contain voids. Many materials exist in nature as flakes, pellets, or granules. Voids are regions which contain something other than

1537-407: The bottom of a fluid results in convection of the heat from the bottom to the top, due to the decrease in the density of the heated fluid, which causes it to rise relative to denser unheated material. The reciprocal of the density of a substance is occasionally called its specific volume , a term sometimes used in thermodynamics . Density is an intensive property in that increasing the amount of

1590-416: The case of non-compact materials, one must also take care in determining the mass of the material sample. If the material is under pressure (commonly ambient air pressure at the earth's surface) the determination of mass from a measured sample weight might need to account for buoyancy effects due to the density of the void constituent, depending on how the measurement was conducted. In the case of dry sand, sand

1643-405: The considered material. Commonly the void is air, but it could also be vacuum, liquid, solid, or a different gas or gaseous mixture. The bulk volume of a material —inclusive of the void space fraction — is often obtained by a simple measurement (e.g. with a calibrated measuring cup) or geometrically from known dimensions. Mass divided by bulk volume determines bulk density . This is not

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1696-975: The definitions of density ( m = ρ V {\displaystyle m=\rho V} ), molar concentration ( n = C V {\displaystyle n=CV} ), and molar mass ( m = M n {\displaystyle m=Mn} ), one can also derive mass flow or molar flow (i.e. standard volume flow): Δ P = k ρ Q 2 = k 1 ρ m ˙ 2 = k ρ C 2 n ˙ 2 = k M C n ˙ 2 . {\displaystyle {\begin{aligned}\Delta P&=k\,\rho \,Q^{2}\\&=k{\frac {1}{\rho }}\,{\dot {m}}^{2}\\&=k{\frac {\rho }{C^{2}}}\,{\dot {n}}^{2}=k{\frac {M}{C}}\,{\dot {n}}^{2}.\end{aligned}}} However, measurements outside

1749-710: The density can be calculated. One dalton per cubic ångström is equal to a density of 1.660 539 066 60 g/cm . A number of techniques as well as standards exist for the measurement of density of materials. Such techniques include the use of a hydrometer (a buoyancy method for liquids), Hydrostatic balance (a buoyancy method for liquids and solids), immersed body method (a buoyancy method for liquids), pycnometer (liquids and solids), air comparison pycnometer (solids), oscillating densitometer (liquids), as well as pour and tap (solids). However, each individual method or technique measures different types of density (e.g. bulk density, skeletal density, etc.), and therefore it

1802-427: The density of a liquid or a gas, a hydrometer , a dasymeter or a Coriolis flow meter may be used, respectively. Similarly, hydrostatic weighing uses the displacement of water due to a submerged object to determine the density of the object. If the body is not homogeneous, then its density varies between different regions of the object. In that case the density around any given location is determined by calculating

1855-488: The density of a small volume around that location. In the limit of an infinitesimal volume the density of an inhomogeneous object at a point becomes: ρ ( r → ) = d m / d V {\displaystyle \rho ({\vec {r}})=dm/dV} , where d V {\displaystyle dV} is an elementary volume at position r → {\displaystyle {\vec {r}}} . The mass of

1908-1020: The design point must compensate for the effects of temperature, pressure, and molar mass on density and concentration. The ideal gas law is used to relate actual values to design values : C = P R T = ( P P ⊖ ) ( T T ⊖ ) C ⊖ {\displaystyle C={\frac {P}{RT}}={\frac {\left({\frac {P}{P^{\ominus }}}\right)}{\left({\frac {T}{T^{\ominus }}}\right)}}C^{\ominus }} ρ = M P R T = ( M M ⊖ P P ⊖ ) ( T T ⊖ ) ρ ⊖ . {\displaystyle \rho ={\frac {MP}{RT}}={\frac {\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)}{\left({\frac {T}{T^{\ominus }}}\right)}}\rho ^{\ominus }.} Substituting these two relations into

1961-1532: The end of the 19th century. While working for the Holyoke Water Power Company , Herschel would develop the means for measuring these flows to determine the water power consumption of different mills on the Holyoke Canal System , first beginning development of the device in 1886, two years later he would describe his invention of the Venturi meter to William Unwin in a letter dated June 5, 1888. Fundamentally, pressure-based meters measure kinetic energy density. Bernoulli's equation (used above) relates this to mass density and volumetric flow: Δ P = 1 2 ρ ( v 2 2 − v 1 2 ) = 1 2 ρ ( ( A 1 A 2 ) 2 − 1 ) v 1 2 = 1 2 ρ ( 1 A 2 2 − 1 A 1 2 ) Q 2 = k ρ Q 2 {\displaystyle \Delta P={\frac {1}{2}}\rho (v_{2}^{2}-v_{1}^{2})={\frac {1}{2}}\rho \left(\left({\frac {A_{1}}{A_{2}}}\right)^{2}-1\right)v_{1}^{2}={\frac {1}{2}}\rho \left({\frac {1}{A_{2}^{2}}}-{\frac {1}{A_{1}^{2}}}\right)Q^{2}=k\,\rho \,Q^{2}} where constant terms are absorbed into k . Using

2014-401: The flow rate can be determined, as in various flow measurement devices such as Venturi meters, Venturi nozzles and orifice plates . Referring to the adjacent diagram, using Bernoulli's equation in the special case of steady, incompressible, inviscid flows (such as the flow of water or other liquid, or low-speed flow of gas) along a streamline, the theoretical pressure drop at the constriction

2067-1396: The flow rate of liquids. A Venturi can be used to measure the volumetric flow rate , Q {\displaystyle \scriptstyle Q} , using Bernoulli's principle . Since Q = v 1 A 1 = v 2 A 2 p 1 − p 2 = ρ 2 ( v 2 2 − v 1 2 ) {\displaystyle {\begin{aligned}Q&=v_{1}A_{1}=v_{2}A_{2}\\[3pt]p_{1}-p_{2}&={\frac {\rho }{2}}\left(v_{2}^{2}-v_{1}^{2}\right)\end{aligned}}} then Q = A 1 2 ρ ⋅ p 1 − p 2 ( A 1 A 2 ) 2 − 1 = A 2 2 ρ ⋅ p 1 − p 2 1 − ( A 2 A 1 ) 2 {\displaystyle Q=A_{1}{\sqrt {{\frac {2}{\rho }}\cdot {\frac {p_{1}-p_{2}}{\left({\frac {A_{1}}{A_{2}}}\right)^{2}-1}}}}=A_{2}{\sqrt {{\frac {2}{\rho }}\cdot {\frac {p_{1}-p_{2}}{1-\left({\frac {A_{2}}{A_{1}}}\right)^{2}}}}}} A Venturi can also be used to mix

2120-494: The following: Density Density ( volumetric mass density or specific mass ) is a substance's mass per unit of volume . The symbol most often used for density is ρ (the lower case Greek letter rho ), although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume: ρ = m V , {\displaystyle \rho ={\frac {m}{V}},} where ρ

2173-419: The gods and replacing it with another, cheaper alloy . Archimedes knew that the irregularly shaped wreath could be crushed into a cube whose volume could be calculated easily and compared with the mass; but the king did not approve of this. Baffled, Archimedes is said to have taken an immersion bath and observed from the rise of the water upon entering that he could calculate the volume of the gold wreath through

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2226-404: The local sonic velocity, thus allowing increased mass flow rate, but only if the nozzle area is also increased to compensate for the resulting decrease in density. The Bernoulli equation is invertible, and pressure should rise when a fluid slows down. Nevertheless, if there is an expansion of the tube section, turbulence will appear, and the theorem will not hold. In all experimental Venturi tubes,

2279-433: The majority of the turbines at the pass. The area hosts a multitude of wind farms, comprising one of California's largest wind resource areas. The pass is undergoing much repowering activity. The area has multiple generations of wind turbine technology installed, including both single and double-blade turbines, as well as the more modern three-blade horizontal axis design. The older generation turbines generate kilowatts, and

2332-588: The modern turbines installed generate up to 3 megawatts, depending on the specific turbine and manufacturer. The Tehachapi Wind Resource Area is a net exporter of generation to other parts of the state of California. A state initiative to upgrade the transmission out of Tehachapi (the 4.5 GW Tehachapi Renewable Transmission Project ) began in 2008 and was completed by 2016. This has opened the door to further regional wind power development up to 10 GW, and multiple solar and storage projects are expected to be installed to utilize that capacity. A prime location for viewing

2385-416: The pressure always increases the density of a material. Increasing the temperature generally decreases the density, but there are notable exceptions to this generalization. For example, the density of water increases between its melting point at 0 °C and 4 °C; similar behavior is observed in silicon at low temperatures. The effect of pressure and temperature on the densities of liquids and solids

2438-523: The pressure in the entrance is compared to the pressure in the middle section; the output section is never compared with them. The simplest apparatus is a tubular setup known as a Venturi tube or simply a Venturi (plural: "Venturis" or occasionally "Venturies"). Fluid flows through a length of pipe of varying diameter. To avoid undue aerodynamic drag , a Venturi tube typically has an entry cone of 30 degrees and an exit cone of 5 degrees. Venturi tubes are often used in processes where permanent pressure loss

2491-2804: The pressure-flow equations above yields the fully compensated flows: Δ P = k ( M M ⊖ P P ⊖ ) ( T T ⊖ ) ρ ⊖ Q 2 = Δ P max ( M M ⊖ P P ⊖ ) ( T T ⊖ ) ( Q Q max ) 2 = k ( T T ⊖ ) ( M M ⊖ P P ⊖ ) ρ ⊖ m ˙ 2 = Δ P max ( T T ⊖ ) ( M M ⊖ P P ⊖ ) ( m ˙ m ˙ max ) 2 = k M ( T T ⊖ ) ( P P ⊖ ) C ⊖ n ˙ 2 = Δ P max ( M M ⊖ T T ⊖ ) ( P P ⊖ ) ( n ˙ n ˙ max ) 2 . {\displaystyle {\begin{aligned}\Delta P&=k{\frac {\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)}{\left({\frac {T}{T^{\ominus }}}\right)}}\rho ^{\ominus }\,Q^{2}&=\Delta P_{\max }{\frac {\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)}{\left({\frac {T}{T^{\ominus }}}\right)}}\left({\frac {Q}{Q_{\max }}}\right)^{2}\\&=k{\frac {\left({\frac {T}{T^{\ominus }}}\right)}{\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)\rho ^{\ominus }}}{\dot {m}}^{2}&=\Delta P_{\max }{\frac {\left({\frac {T}{T^{\ominus }}}\right)}{\left({\frac {M}{M^{\ominus }}}{\frac {P}{P^{\ominus }}}\right)}}\left({\frac {\dot {m}}{{\dot {m}}_{\max }}}\right)^{2}\\&=k{\frac {M\left({\frac {T}{T^{\ominus }}}\right)}{\left({\frac {P}{P^{\ominus }}}\right)C^{\ominus }}}{\dot {n}}^{2}&=\Delta P_{\max }{\frac {\left({\frac {M}{M^{\ominus }}}{\frac {T}{T^{\ominus }}}\right)}{\left({\frac {P}{P^{\ominus }}}\right)}}\left({\frac {\dot {n}}{{\dot {n}}_{\max }}}\right)^{2}.\end{aligned}}} Q , m , or n are easily isolated by dividing and taking

2544-402: The same thing as the material volumetric mass density. To determine the material volumetric mass density, one must first discount the volume of the void fraction. Sometimes this can be determined by geometrical reasoning. For the close-packing of equal spheres the non-void fraction can be at most about 74%. It can also be determined empirically. Some bulk materials, however, such as sand, have

2597-460: The stories they tell about the lake in Palestine it would further bear out what I say. For they say if you bind a man or beast and throw him into it he floats and does not sink beneath the surface. In a well-known but probably apocryphal tale, Archimedes was given the task of determining whether King Hiero 's goldsmith was embezzling gold during the manufacture of a golden wreath dedicated to

2650-426: The substance floats in water. The density of a material varies with temperature and pressure. This variation is typically small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object and thus increases its density. Increasing the temperature of a substance (with a few exceptions) decreases its density by increasing its volume. In most materials, heating

2703-584: The turbines is off of State Route 58 and from Tehachapi-Willow Springs Road. One proponent for further regional wind power development is Southern California Edison , which executed power purchase agreements for up to 1,500 megawatts (MW) or more of power generated from new projects to be built in the Tehachapi area, of which the Alta Wind Energy Center was developed. The 2006 contract, which more than doubles SCE's wind energy portfolio, envisions more than 50 square miles (130 km) of wind parks in

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2756-546: The value in (kg/m ). Liquid water has a density of about 1 kg/dm , making any of these SI units numerically convenient to use as most solids and liquids have densities between 0.1 and 20 kg/dm . In US customary units density can be stated in: Imperial units differing from the above (as the Imperial gallon and bushel differ from the US units) in practice are rarely used, though found in older documents. The Imperial gallon

2809-443: Was based on the concept that an Imperial fluid ounce of water would have a mass of one Avoirdupois ounce, and indeed 1 g/cm ≈ 1.00224129 ounces per Imperial fluid ounce = 10.0224129 pounds per Imperial gallon. The density of precious metals could conceivably be based on Troy ounces and pounds, a possible cause of confusion. Knowing the volume of the unit cell of a crystalline material and its formula weight (in daltons ),

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