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Compression (physics)
Compression (physics)
Compression (physics)
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Uniaxial compression

In mechanics, compression is the application of balanced inward ("pushing") forces to different points on a material or structure, that is, forces with no net sum or torque directed so as to reduce its size in one or more directions.[1] It is contrasted with tension or traction, the application of balanced outward ("pulling") forces; and with shearing forces, directed so as to displace layers of the material parallel to each other. The compressive strength of materials and structures is an important engineering consideration.

In uniaxial compression, the forces are directed along one direction only, so that they act towards decreasing the object's length along that direction.[2] The compressive forces may also be applied in multiple directions; for example inwards along the edges of a plate or all over the side surface of a cylinder, so as to reduce its area (biaxial compression), or inwards over the entire surface of a body, so as to reduce its volume.

Technically, a material is under a state of compression, at some specific point and along a specific direction , if the normal component of the stress vector across a surface with normal direction is directed opposite to . If the stress vector itself is opposite to , the material is said to be under normal compression or pure compressive stress along . In a solid, the amount of compression generally depends on the direction , and the material may be under compression along some directions but under traction along others. If the stress vector is purely compressive and has the same magnitude for all directions, the material is said to be under isotropic compression, hydrostatic compression, or bulk compression. This is the only type of static compression that liquids and gases can bear.[3] It affects the volume of the material, as quantified by the bulk modulus and the volumetric strain.

The inverse process of compression is called decompression, dilation, or expansion, in which the object enlarges or increases in volume.

In a mechanical wave, which is longitudinal, the medium is displaced in the wave's direction, resulting in areas of compression and rarefaction.

Effects

[edit]

When put under compression (or any other type of stress), every material will suffer some deformation, even if imperceptible, that causes the average relative positions of its atoms and molecules to change. The deformation may be permanent, or may be reversed when the compression forces disappear. In the latter case, the deformation gives rise to reaction forces that oppose the compression forces, and may eventually balance them.[4]

Liquids and gases cannot bear steady uniaxial or biaxial compression, they will deform promptly and permanently and will not offer any permanent reaction force. However they can bear isotropic compression, and may be compressed in other ways momentarily, for instance in a sound wave.

Tightening a corset applies biaxial compression to the waist.

Every ordinary material will contract in volume when put under isotropic compression, contract in cross-section area when put under uniform biaxial compression, and contract in length when put into uniaxial compression. The deformation may not be uniform and may not be aligned with the compression forces. What happens in the directions where there is no compression depends on the material.[4] Most materials will expand in those directions, but some special materials will remain unchanged or even contract. In general, the relation between the stress applied to a material and the resulting deformation is a central topic of continuum mechanics.

Uses

[edit]
Compression test on a universal testing machine

Compression of solids has many implications in materials science, physics and structural engineering, for compression yields noticeable amounts of stress and tension.

By inducing compression, mechanical properties such as compressive strength or modulus of elasticity, can be measured.[5]

Compression machines range from very small table top systems to ones with over 53 MN capacity.

Gases are often stored and shipped in highly compressed form, to save space. Slightly compressed air or other gases are also used to fill balloons, rubber boats, and other inflatable structures. Compressed liquids are used in hydraulic equipment and in fracking.

In engines

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Internal combustion engines

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In internal combustion engines the explosive mixture gets compressed before it is ignited; the compression improves the efficiency of the engine. In the Otto cycle, for instance, the second stroke of the piston effects the compression of the charge which has been drawn into the cylinder by the first forward stroke.[6]

Steam engines

[edit]

The term is applied to the arrangement by which the exhaust valve of a steam engine is made to close, shutting a portion of the exhaust steam in the cylinder, before the stroke of the piston is quite complete. This steam being compressed as the stroke is completed, a cushion is formed against which the piston does work while its velocity is being rapidly reduced, and thus the stresses in the mechanism due to the inertia of the reciprocating parts are lessened.[7] This compression, moreover, obviates the shock which would otherwise be caused by the admission of the fresh steam for the return stroke.

See also

[edit]

References

[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Compression (physics)

View on Grokipedia
from Grokipedia
In physics, compression refers to the application of a force that reduces the volume or linear dimensions of a by squeezing it together, resulting in an increase in and . This process is governed by the 's elastic properties and is distinct from tension, which elongates objects; materials must withstand both to be structurally useful. In solids and liquids, compression deforms the atomic or molecular structure against strong electromagnetic forces, typically producing small volume changes unless extreme pressures are applied. The resistance to uniform compression is quantified by the bulk modulus KK, defined as K=−ΔPΔV/VK = -\frac{\Delta P}{\Delta V / V}, where ΔP\Delta P is the change in pressure and ΔV/V\Delta V / V is the fractional volume change; higher values indicate greater incompressibility, as seen in materials like steel (K≈130−160K \approx 130{-}160 GPa) versus water (K≈2.2K \approx 2.2 GPa). In gases, compression more readily reduces intermolecular distances, often modeled as an adiabatic process where volume decrease raises both pressure and temperature, following p2p1=(V1V2)γ\frac{p_2}{p_1} = \left( \frac{V_1}{V_2} \right)^\gamma with γ≈1.4\gamma \approx 1.4 for air. Compression plays a central role in diverse physical phenomena and applications, from the elastic deformation in —where σ=F/A\sigma = F/A (force over area) induces strain ϵ=ΔL/L\epsilon = \Delta L / L—to thermodynamic cycles in engines, shock wave propagation in solids, and even biological tissues under load. In nonlinear materials, such as wood or polymers, compression can lead to or plastic yielding, highlighting the interplay between elastic recovery and permanent deformation.

Fundamental Concepts

Definition and Principles

In physics, compression refers to the process of applying a force to a substance—whether gas, , or —that reduces its , thereby increasing its and . This occurs when inward forces act on the , squeezing its constituent particles closer together, as opposed to expansion where forces pull particles apart. Compressive forces are governed by Newton's third law of motion, which states that for every action force applied to compress the substance, there is an equal and opposite reaction force from the substance resisting the deformation. Unlike tensile forces, which elongate a by pulling it apart, or shear forces, which cause sliding or angular distortion without net change, compression specifically targets volumetric reduction through balanced inward . The foundational principles of compression were explored in the through early experiments on gases, notably by in 1662. Boyle's observations, detailed in his work New Experiments Physico-Mechanicall, Touching the Spring of the Air, and its Effects, revealed that for a fixed of gas at constant , the and are inversely proportional, leading to what is now known as . This empirical relationship is expressed mathematically as P1V1=P2V2P_1 V_1 = P_2 V_2, where P1P_1 and V1V_1 are the initial and , and P2P_2 and V2V_2 are the final values after compression. Boyle's law can be derived from the , which posits that gas arises from the collisions of molecules with container walls. In this model, the PP is proportional to the of molecules (number per unit ) times the squared speed of the molecules, P∝NVv2P \propto \frac{N}{V} v^2, where NN is the number of molecules and VV is the . At constant , the molecular speeds remain unchanged, so halving the doubles the NV\frac{N}{V}, thereby doubling the to maintain the product PVP V constant. This derivation, originally conceptualized by in 1738 and refined by later physicists like James Clerk Maxwell, underscores how compression increases intermolecular interactions without altering thermal energy in isothermal conditions. Relevant quantities in compression are measured using standard International System of Units (SI): pressure in pascals (Pa, where 1 Pa = 1 N/m²), volume in cubic meters (m³), and applied force in newtons (N, where 1 N = 1 kg·m/s²). These units facilitate precise quantification across gases, liquids, and solids, though the ease of compression varies by phase—gases compress readily due to large intermolecular spaces, while solids and liquids resist more due to tighter atomic packing.

Compression Ratio

The is a dimensionless that quantifies the extent of reduction during a compression in physical systems, defined as the of the initial V1V_1 to the final V2V_2, expressed as r=V1V2r = \frac{V_1}{V_2}. This measure is fundamental in analyzing how compression alters the state of a substance, particularly gases, by indicating the factor by which the is diminished./University_Physics_II_-Thermodynamics_Electricity_and_Magnetism(OpenStax)/03%3A_The_First_Law_of_Thermodynamics/3.07%3A_Adiabatic_Processes_for_an_Ideal_Gas) In practical setups such as piston-cylinder arrangements, the compression ratio is calculated using the formula r=Vs+VcVcr = \frac{V_s + V_c}{V_c}, where VsV_s represents the swept volume (the volume displaced by the piston) and VcV_c is the clearance volume (the residual volume at the end of compression). This formulation accounts for the geometry of the system and is widely used to characterize the compression capability in mechanical devices. The significance of the lies in its role as an indicator of potential in achieving reduction, with higher values generally leading to substantial increases according to the . However, excessively high ratios can impose severe stresses, risking material failure through mechanisms like or in the containing structures. In physics experiments on gas compression, typical ratios range from 2 to 10, allowing observable changes in and without overwhelming the apparatus; for instance, a of 5 is common in demonstrations of adiabatic compression to illustrate thermodynamic principles./University_Physics_II_-Thermodynamics_Electricity_and_Magnetism(OpenStax)/03%3A_The_First_Law_of_Thermodynamics/3.07%3A_Adiabatic_Processes_for_an_Ideal_Gas) This is most applicable to compressible media like gases, where significant changes occur; for incompressible fluids such as liquids, absent phase transitions, the ratio approaches 1 due to minimal alteration under , rendering it impractical for quantification in such cases.

Thermodynamic Processes

Isothermal Compression

Isothermal compression refers to a in which a gas is compressed while its remains constant, necessitating the continuous rejection of to the surroundings to maintain . This process is idealized and assumes the gas behaves as an , where intermolecular forces and of the gas molecules are negligible. The thermodynamic foundation of isothermal compression is rooted in the ideal gas law, expressed as PV=nRTPV = nRT, where PP is pressure, VV is volume, nn is the number of moles, RR is the gas constant, and TT is the constant temperature. For a reversible isothermal compression, the work done on the gas, WW, is given by the formula W=nRTln⁡(V1V2),W = nRT \ln\left(\frac{V_1}{V_2}\right), where V1V_1 is the initial volume and V2V_2 is the final volume (V2<V1V_2 < V_1). This expression arises from integrating the reversible work dW=P dVdW = P \, dV along the path where P=nRTVP = \frac{nRT}{V}. The derivation follows from the first law of , ΔU=Q+W\Delta U = Q + W, where ΔU\Delta U is the change in , QQ is added to the system, and WW is work done on the system. For an undergoing isothermal compression, ΔU=0\Delta U = 0 because internal energy depends only on , which is constant. Thus, Q=−WQ = -W, meaning the heat rejected to the surroundings equals the work input in magnitude but opposite in sign. On a pressure-volume (P-V) diagram, the isothermal compression path appears as a hyperbolic curve, reflecting the inverse relationship PV=constantPV = \text{constant} at fixed . The area under this curve represents the work done during the process. In practice, true isothermal compression is approximated by conducting the process slowly while maintaining contact with a , such as in the isothermal compression step of an ideal Carnot refrigeration cycle. As a reversible , isothermal compression requires the minimum work input compared to an irreversible or adiabatic compression for the same volume change, enhancing efficiency in theoretical analyses.

Adiabatic Compression

Adiabatic compression is a in which a gas is compressed without any exchange with its surroundings, denoted by [Q](/page/Q)=0[Q](/page/Q) = 0, resulting in an increase in the and of the gas. This occurs when the compression is sufficiently rapid or the is well-insulated, preventing with the environment. In contrast to processes involving , such as isothermal compression, adiabatic compression leads to a temperature rise due to the work done on the . For an undergoing reversible adiabatic compression, the process follows Poisson's equations, which describe the relationships between , , and . The key relation is PVγ=constantPV^\gamma = \text{constant}, where γ=Cp/Cv\gamma = C_p / C_v is the ratio of specific heats at constant (CpC_p) and constant (CvC_v). Another form is TVγ−1=constantTV^{\gamma-1} = \text{constant}, linking and directly. These equations arise from of , ΔU=Q−W\Delta U = Q - W, where for an Q=0Q = 0, so ΔU=−W\Delta U = -W (with WW as work done by the system). For an , the change in is ΔU=nCvΔT\Delta U = n C_v \Delta T, and the work for a reversible process is W=∫P dVW = \int P \, dV. Substituting P=nRT/VP = nRT / V and using dU=nCvdTdU = n C_v dT leads to CvdT+PdV=0C_v dT + P dV = 0, which integrates to the Poisson relations assuming constant γ\gamma. On a pressure-volume (P-V) diagram, the adiabatic compression curve is steeper than the corresponding isothermal curve for the same volume change, indicating a higher final for a given because no is removed to maintain constant . This steeper slope reflects the increasing more rapidly due to the rising during compression. Examples of adiabatic compression include the formation of shock waves in gases, where a sudden increase propagates as a discontinuity, compressing the gas nearly adiabatically and heating it abruptly. Another example is the rapid compression of gas by a suddenly moving in a , mimicking insulated conditions and demonstrating the increase without external input. In physics, the focus is often on reversible adiabatic compression, which assumes quasi-static changes with no or , allowing the system to remain in equilibrium throughout and strictly following the Poisson equations. Irreversible adiabatic compression, such as in real shock waves or rapid motions, involves generation and deviates from these ideal relations, but the reversible case idealizes the process for theoretical analysis.

Mechanical Properties

In Gases

Gases are highly compressible materials, capable of undergoing substantial volume reductions under applied due to their low and large intermolecular distances. At low densities and moderate pressures, gases approximate ideal behavior as described by the , PV=nRTPV = nRT, where volume is inversely proportional to pressure, allowing for significant compression without structural resistance. This contrasts with the near-incompressibility of and liquids, enabling gases to fill containers flexibly and respond readily to external forces. Gases exhibit near-perfect elasticity during compression, returning to their original volume upon release of pressure, as their molecular structure lacks rigid bonding and relies on kinetic motion for volume maintenance. This elastic response is analogous to for volumetric deformation, where the change in volume is proportional to the applied stress for small strains. The KK, defined as K=−VdPdVK = -V \frac{dP}{dV}, measures this resistance to compression; for gases, the high results in a low KK, such as approximately 1.4×1051.4 \times 10^5 Pa for air under adiabatic conditions at . At high pressures, real gases deviate from ideal behavior, requiring corrections via the Z=PVnRTZ = \frac{PV}{nRT}, which accounts for intermolecular attractions and finite molecular volume; Z<1Z < 1 indicates reduced compressibility compared to ideal predictions. The modifies the to incorporate these effects: (P+aVm2)(Vm−b)=RT,\left( P + \frac{a}{V_m^2} \right) (V_m - b) = RT, where VmV_m is the , aa represents attractive forces, and bb the per mole. Under extreme compression, particularly if the is below the critical point, gases can undergo phase transitions to liquids, for example, can be liquefied by compression at temperatures below its critical point of 31.1°C and 73 atm.

In Solids and Liquids

Solids and liquids exhibit significantly lower compared to gases, primarily due to their denser molecular structures and stronger intermolecular forces, which resist changes under applied . In liquids, such as , the reduction is minimal; for instance, compresses by approximately 5% under a pressure of 1000 atmospheres (about 101 MPa). This near-incompressibility arises from the high KK, defined as K=−ΔPΔV/VK = -\frac{\Delta P}{\Delta V / V}, where ΔP\Delta P is the change in and ΔV/V\Delta V / V is the fractional change. For , K≈2.2×109K \approx 2.2 \times 10^9 Pa at . In solids, compression similarly induces limited volumetric changes, governed by the material's , which is typically much higher than that of liquids. For example, has a bulk modulus of approximately 1.6×10111.6 \times 10^{11} Pa, making it over 70 times more resistant to compression than . Under compressive stress, solids initially undergo elastic deformation, where the strain ε\varepsilon is linearly proportional to the stress σ\sigma according to : σ=Eε\sigma = E \varepsilon, with EE being the . This elastic regime allows the material to return to its original shape upon stress removal, provided the stress remains below the yield point. Beyond the elastic limit, solids transition to plastic deformation, where permanent shape changes occur, or to if the is exceeded. For structural materials like , the typically ranges from 20 to 40 MPa, beyond which cracking and failure initiate. In practical applications, this low of liquids is exploited in hydraulic presses, where incompressible s transmit force efficiently according to Pascal's principle, enabling the amplification of mechanical for tasks like metal forming without significant fluid volume change. Compression ratios in liquids rarely exceed 1.1 due to their inherent resistance to densification. Failure modes under compression differ markedly between solids and liquids. In slender solids, such as columns, can occur as an instability before reaching the material's yield strength, leading to sudden lateral deflection and collapse under axial loads. For liquids under rapid compression, emerges as a key failure mechanism, where localized pressure drops below the cause the formation and violent collapse of vapor bubbles, generating shock waves that can erode surfaces or damage equipment.

Engineering Applications

Internal Combustion Engines

In internal combustion engines, the compression stroke is essential for elevating the pressure and temperature of the air-fuel mixture, enabling controlled ignition and maximizing energy extraction from combustion. This process occurs in reciprocating piston engines, where the piston compresses the mixture within the cylinder during the compression phase of the four-stroke cycle, preparing it for efficient burning. The concept traces back to Nikolaus Otto's invention of the four-stroke engine in 1876, which laid the foundation for spark-ignition systems, and Rudolf Diesel's development of the compression-ignition engine in the 1890s, which relied on extreme compression for auto-ignition. The , predominant in , involves adiabatic compression of the premixed air-fuel charge, followed by constant-volume heat addition via spark ignition near top dead center. Typical compression ratios in these range from 8 to 12, balancing efficiency gains against practical limits imposed by fuel properties and design. This configuration allows for rapid in a , converting into mechanical work as the expanding gases drive the downward. In contrast, the , used in diesel engines, compresses only air adiabatically to much higher ratios of 14 to 25, raising its temperature sufficiently for and spontaneous ignition without a . is introduced post-compression, leading to constant-pressure heat addition, which supports higher efficiencies in heavy-duty applications. This higher compression enables diesel engines to operate more efficiently under varying loads compared to Otto-cycle engines. The physics of compression in both cycles approximates an adiabatic process, where no heat is exchanged with the surroundings, leading to a thermal efficiency expressed as η=1−(1r)γ−1\eta = 1 - \left( \frac{1}{r} \right)^{\gamma - 1} with rr as the compression ratio and γ\gamma (approximately 1.4 for air) as the ratio of specific heats. However, excessive temperature rise during compression can cause knocking—uncontrolled auto-ignition of the end-gas mixture—resulting in pressure spikes and potential engine damage; this is addressed by selecting fuels with higher octane ratings that resist premature ignition.

Steam Engines

In reciprocating steam engines, compression serves to manage the residual exhaust trapped in the cylinder's clearance volume after the exhaust stroke, thereby reducing work losses from pressure mismatches during the subsequent intake. This residual , which occupies a small but significant portion of the cylinder volume, is recompressed by the advancing piston to a pressure approaching that of the incoming supply , preventing irreversible expansion or compression losses when fresh enters. As part of the practical in these engines, this step enhances thermodynamic efficiency by aligning exhaust and admission pressures, minimizing the energy penalty associated with clearance volume effects. Mechanically, the performs this compression during the latter part of the exhaust-return , with typical compression ratios ranging from 1.5 to 3 to balance the benefits against added work input. These ratios are chosen to limit clearance losses while avoiding excessive compression work, as higher ratios would increase the required without proportional gains in cycle performance. In practice, the process occurs in the low-pressure cylinder of compound designs, where the piston's motion compresses the against the closed inlet valves until equilibrium is neared. Physically, the compression is nearly isothermal due to conductive from the cylinder walls, which are often cooled by surrounding air or jackets to maintain operational temperatures. For these low compression ratios, the work input is approximated as W≈PΔVW \approx P \Delta V, where PP is the average and ΔV\Delta V is the change in , reflecting the modest pressure rise and minimal temperature deviation from isothermality. This approximation holds because the process deviates little from constant pressure over small volume changes, contrasting with adiabatic assumptions in higher-ratio systems. The process approximates isothermal compression principles, enabling efficient recompression of with reduced generation. Compound steam engines, such as those employing Woolf or Corliss configurations, incorporate multi-stage compression across multiple cylinders to further approach isothermal efficiency limits. In Woolf designs, high- and low-pressure cylinders sequence the compression of residual , distributing the work to lower overall irreversibilities and better emulate ideal rejection. Corliss engines enhance this through advanced , which optimizes compression timing and reduces clearance-related losses, achieving up to 30% better than simple engines by integrating staged pressure management. A pivotal historical advancement came in the 1760s with James Watt's introduction of the separate condenser, which lowered exhaust and thereby facilitated more effective compression by reducing the initial pressure against which the piston must work. This innovation minimized heat losses in the cylinder during exhaust and allowed residual steam to be compressed from a lower baseline, boosting net work output. Overall, such compression strategies reduce across the cycle, increasing the and elevating the engine's work output by 10-20% in practical setups compared to non-compressing designs.

Industrial Compressors

Industrial compressors are specialized machines designed for large-scale gas compression in various sectors, primarily utilizing reciprocating and centrifugal types to handle high volumes and pressures efficiently. These devices operate on principles of positive displacement or dynamic compression, enabling applications from process industries to energy . Reciprocating compressors function through piston-based mechanisms within cylinders, drawing in gas during the stroke and compressing it via to reduce volume and increase . As positive displacement machines, they trap a fixed volume of gas and compress it intermittently, making them suitable for high- requirements. For elevated overall compression ratios, multi-stage configurations are employed, with each stage limited to ratios up to approximately 8:1 to manage loads and mechanical stresses. The compression process in these units follows a polytropic path, described by the relation PVn=constantPV^n = \text{constant}, where nn is the polytropic exponent ranging between 1 (isothermal) and γ\gamma (adiabatic specific heat ratio), typically 1.1 to 1.21 in practical hermetic designs. Intercooling between stages dissipates , approximating isothermal conditions to reduce work input and improve . Centrifugal compressors, in contrast, are dynamic machines that provide continuous flow by accelerating gas through a rotating , converting into via diffusion in a downstream or diffuser. The fundamental mechanics derive from an adapted form of Euler's turbomachinery equation, where the HH arises from changes in tangential velocity components imparted by the impeller blades. A simplified expression for the head in ideal cases without inlet swirl is H=U22gH = \frac{U_2^2}{g}, with U2U_2 as the impeller tip peripheral speed and gg as , highlighting the velocity-induced pressure rise central to their operation. Multi-stage arrangements stack s axially to achieve higher heads for demanding flows. In applications such as pipelines, industrial compressors boost pressure across multiple stations, enabling overall compression ratios exceeding 100:1 through sequential staging to maintain long-distance flow against frictional losses. variants support processes, powering pneumatic tools, , and in sectors like automotive and pharmaceuticals. Efficiency in industrial compressors is quantified by isentropic efficiency η\eta, defined as the ratio of actual shaft work to the ideal isentropic work for the same pressure rise, typically ranging from 70% to 90% depending on design and conditions. This metric underscores losses from irreversibilities like and , with higher values achieved in well-maintained, large-scale units. Safety concerns in dynamic compressors like centrifugal types include surge and , instabilities triggered by mismatched flow rates where axial flow reverses or tangential disruptions reduce blade lift, potentially causing severe mechanical damage. Anti-surge controls, such as recycle valves, maintain adequate flow margins to prevent these events during off-design operations.

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  68. https://petrotechinc.com/centrifugal-compressor-efficiency/
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