Hubbry Logo
Poise (unit)Poise (unit)Main
Open search
Poise (unit)
Community hub
Poise (unit)
logo
7 pages, 0 posts
0 subscribers
Be the first to start a discussion here.
Be the first to start a discussion here.
Poise (unit)
Poise (unit)
Poise (unit)
View on Wikipedia
from Wikipedia
poise
Unit systemCentimetre–gram–second system of units
Unit ofDynamic viscosity
SymbolP
Named afterJean Léonard Marie Poiseuille
Derivation1 P = 1 dyn⋅s/cm2
Conversions
1 P in ...... is equal to ...
   CGS base units   1 cm−1⋅g⋅s−1
   SI units   0.1 Pa⋅s

The poise (symbol P; /pɔɪz, pwɑːz/) is the unit of dynamic viscosity (absolute viscosity) in the centimetre–gram–second system of units (CGS).[1] It is named after Jean Léonard Marie Poiseuille (see Hagen–Poiseuille equation). The centipoise (1 cP = 0.01 P) is more commonly used than the poise itself.

Dynamic viscosity has dimensions of , that is, .

The analogous unit in the International System of Units is the pascal-second (Pa⋅s):[2]

The poise is often used with the metric prefix centi- because the viscosity of water at 20 °C (standard conditions for temperature and pressure) is almost exactly 1 centipoise.[3] A centipoise is one hundredth of a poise, or one millipascal-second (mPa⋅s) in SI units (1 cP = 10−3 Pa⋅s = 1 mPa⋅s).[4]

The CGS symbol for the centipoise is cP. The abbreviations cps, cp, and cPs are sometimes seen.

Liquid water has a viscosity of 0.00890 P at 25 °C at a pressure of 1 atmosphere (0.00890 P = 0.890 cP = 0.890 mPa⋅s).[5]

See also

[edit]
Look up poise in Wiktionary, the free dictionary.

References

[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Poise (unit)

View on Grokipedia
from Grokipedia
The poise (symbol: P) is the unit of dynamic in the centimetre–gram–second (CGS) system of units, named in honour of the French physician and physiologist (1797–1869), who studied flow in capillaries. It is defined as the dynamic viscosity of a that requires a of one per square to produce a velocity gradient of one per second between two parallel planes one apart. One poise is exactly equal to 0.1 pascal-second (Pa·s), the corresponding unit in the (SI). Although the poise remains the base CGS unit for dynamic , practical measurements often employ the centipoise (cP), which is one hundredth of a poise (1 cP = 0.01 P = 1 mPa·s), as most fluids exhibit viscosities in this smaller range—for instance, at 20°C has a dynamic viscosity of approximately 1 cP. The unit plays a key role in , , and engineering applications such as , processing, and biomedical fluid studies, where it quantifies a fluid's resistance to shear deformation. Despite the widespread adoption of SI units, the poise and its derivatives persist in legacy systems, technical literature, and certain industries for consistency with historical data.

Definition and Properties

Core Definition

The poise (symbol: P) is the unit of dynamic , also known as absolute , in the –gram–second (CGS) system of units. It quantifies the internal resistance of a to flow under an applied , serving as a fundamental measure in within the CGS framework. Dynamic represents a 's resistance to and is defined as the ratio of the to the rate of shear strain. This property arises from the frictional forces between adjacent layers moving at different velocities, with higher indicating greater resistance to deformation. In practical terms, it describes how a responds to gradual deformation by shear forces, distinguishing it from kinematic , which also accounts for . The basic formula for dynamic is η=τdudy\eta = \frac{\tau}{\frac{du}{dy}}, where η\eta is the dynamic in poise, τ\tau is the in s per square centimeter, and dudy\frac{du}{dy} is the velocity gradient (rate of shear strain) in centimeters per second per centimeter. One poise is equivalent to one -second per square centimeter (·s/cm²), reflecting the CGS base units of force, time, and length. For context, at 20°C exhibits a dynamic of approximately 0.01 P, equivalent to 1 centipoise, illustrating the scale for common liquids.

Physical Dimensions

The poise, as the CGS unit of dynamic viscosity, has the dimensional formula [η]=ML−1T−1[\eta] = \mathrm{M} \mathrm{L}^{-1} \mathrm{T}^{-1}, where M\mathrm{M} represents mass in grams, L\mathrm{L} length in centimeters, and T\mathrm{T} time in seconds. This formulation arises from the fundamental definition of dynamic viscosity as the ratio of shear stress to velocity gradient in a fluid. To derive these dimensions within the CGS system, consider shear stress τ\tau, which equals force per unit area and is expressed as τ=dynecm2=g⋅cm/s2cm2=g/(cm⋅s2)\tau = \frac{\mathrm{dyne}}{\mathrm{cm}^2} = \frac{\mathrm{g} \cdot \mathrm{cm} / \mathrm{s}^2}{\mathrm{cm}^2} = \mathrm{g} / (\mathrm{cm} \cdot \mathrm{s}^2), yielding dimensions ML−1T−2\mathrm{M} \mathrm{L}^{-1} \mathrm{T}^{-2}. The velocity gradient dudy\frac{du}{dy} has dimensions of reciprocal time, s−1\mathrm{s}^{-1} or T−1\mathrm{T}^{-1}, as it represents change in velocity (length per time) over distance (length). Thus, dynamic viscosity η=τdudy\eta = \frac{\tau}{\frac{du}{dy}} combines to g/(cm⋅s)\mathrm{g} / (\mathrm{cm} \cdot \mathrm{s}) or ML−1T−1\mathrm{M} \mathrm{L}^{-1} \mathrm{T}^{-1}. This dimensional structure integrates , , and time to quantify viscous drag, capturing the 's resistance to shear through the interplay of inertial forces (via ) and spatial-temporal flow rates (via and time inverses). In contrast, kinematic incorporates , resulting in dimensions of L2T−1\mathrm{L}^2 \mathrm{T}^{-1}, but focuses on flow without explicit dependence.

Unit Equivalences

Relation to SI Units

The SI unit of dynamic viscosity is the pascal-second (Pa·s), defined as 1 Pa·s = 1 N·s/m² = 1 kg/(m·s). The poise (P) converts to this unit as 1 P = 0.1 Pa·s, or equivalently, 1 Pa·s = 10 P. This conversion factor of 0.1 stems from the scaling between the CGS and SI (MKS) systems, where the CGS unit of is the (1 = 10^{-5} ) and the unit of area is the square centimeter (1 cm² = 10^{-4} m²), yielding a CGS stress unit of /cm² = 10^{-5} / 10^{-4} m² = 0.1 Pa; since dynamic incorporates this stress divided by shear rate (in s^{-1}), the poise equals 0.1 Pa·s. The poiseuille (Pl) is a proposed SI-derived unit of dynamic viscosity, where 1 Pl = 1 Pa·s = 10 P, distinct from the CGS poise despite sharing a namesake.

Submultiples and Multiples

The poise (P), as the base unit of dynamic viscosity in the centimeter-gram–second (CGS) system, employs standard decimal prefixes to form practical submultiples and multiples for expressing viscosities across a wide range. The centipoise (cP), defined as 1 cP=10−2 P1 \, \mathrm{cP} = 10^{-2} \, \mathrm{P}, is the most commonly used submultiple due to its alignment with typical viscosities of low-viscosity fluids, providing human-scale numerical values that avoid cumbersome decimals when measuring in poise; for instance, water has a viscosity of approximately 1 cP1 \, \mathrm{cP} at 20∘C20^\circ \mathrm{C}. The millipoise (mP), where 1 mP=10−3 P1 \, \mathrm{mP} = 10^{-3} \, \mathrm{P}, serves for even lower viscosities, such as those in dilute gases or highly fluid systems. For multiples, the decapoise (dP or daP), equivalent to 1 dP=10 P1 \, \mathrm{dP} = 10 \, \mathrm{P}, accommodates moderately higher viscosities in the CGS framework. Note that the poiseuille (Pl), the coherent SI unit of dynamic (1 Pl = 1 Pa·s), numerically equals 10 poise and has occasionally been referred to as a decapoise in older , but it belongs to the International System rather than as a CGS multiple. At the upper end, the megapoise (MP), defined as 1 MP=106 P1 \, \mathrm{MP} = 10^6 \, \mathrm{P}, is applied to extremely high viscosities, such as those of solid-like substances like pitch. Common submultiples of the poise are summarized in the following table:
UnitSymbolRelation to Poise
PoiseP1 P1 \, \mathrm{P}
CentipoisecP10−2 P10^{-2} \, \mathrm{P}
MillipoisemP10−3 P10^{-3} \, \mathrm{P}
This structure ensures measurements remain intuitive within the CGS system, with the centipoise particularly favored for its convenience in everyday and laboratory contexts.

Historical Development

Poiseuille's Work

(1797–1869) was a French physician and physiologist renowned for his pioneering studies on blood flow in , which provided foundational insights into the nature of in . Motivated by physiological questions surrounding circulation, Poiseuille conducted meticulous experiments to quantify the resistance encountered by fluids in narrow tubes, simulating capillary conditions. His work emphasized the resistive properties of fluids, laying the groundwork for later quantitative measures of . Poiseuille earned his medical doctorate in 1828 with a thesis titled Recherches sur la force du coeur aortique, in which he explored aortic blood pressure using early manometric techniques, including a mercury-based hemodynamometer tested on animals. This early research sparked his interest in flow resistance, leading to a series of publications between 1840 and 1846. In these, he experimentally derived the relationship for steady laminar flow through cylindrical tubes, expressing the volumetric flow rate QQ as Q=πr4ΔP8ηLQ = \frac{\pi r^4 \Delta P}{8 \eta L}, where rr is the tube radius, ΔP\Delta P is the pressure difference across the tube of length LL, and η\eta is the fluid's coefficient of viscosity; this relationship, known as the Hagen–Poiseuille equation, was independently derived theoretically by Gotthilf Hagen in 1839, and the full form appeared in Poiseuille's 1844 memoir. His experiments involved forcing distilled water through glass capillary tubes of diameters ranging from 0.013 to 0.6 mm under controlled pressures, while employing mercury manometers to measure pressure drops accurately. These investigations demonstrated that flow resistance is inversely proportional to the of the tube radius and directly proportional to , underscoring 's central role in impeding . Poiseuille's primary aim was to elucidate blood circulation in living organisms, particularly how capillary dimensions and 's viscous properties influence physiological transport. Although focused on , his empirical and theoretical contributions proved applicable beyond , influencing broader studies in by establishing as a quantifiable governing flow behavior.

Naming and Adoption

The poise unit of dynamic viscosity was formally proposed in 1913 by British physicists Reginald M. Deeley and Philip H. Parr in their paper on the viscosity of glacier ice, published in the . They suggested naming the centimeter-gram-second (CGS) unit of viscosity—the dyne-second per square centimeter—after to honor his pioneering experimental work on and resistance in capillaries, originally motivated by physiological studies of blood circulation. This naming occurred within the broader context of the CGS system's evolution, where foundational units like the (for ) and erg (for ) had been established earlier by a committee of the British Association for the Advancement of Science in to promote a coherent absolute system of measurement. The unit naturally emerged from these, as dynamic is defined dimensionally as times time per area in CGS terms, aligning with the dyne·s/cm² without requiring a separate name until Poiseuille's contributions warranted recognition. The poise gained widespread adoption in European scientific literature during the and , particularly in and , as experimental viscometry advanced with capillary and rotational methods. For practical use, Deeley and Parr also introduced the centipoise (one-hundredth of a poise) in their proposal, which quickly became the preferred subscale due to the typical range of viscosities encountered in experiments and engineering. Similarly, the related CGS unit for kinematic viscosity was named the stokes in 1928, after George Gabriel Stokes, reflecting parallel efforts to honor key figures in viscous flow theory.

Applications and Usage

In Fluid Dynamics

In , the poise serves as the unit for dynamic η in the centimeter-gram-second (CGS) system, quantifying the resistance of a to during flow. For incompressible Newtonian fluids, η appears in the Navier-Stokes equations, which govern conservation. Specifically, the viscous term is expressed as ∇·(η (∇u + (∇u)^T)), where u is the field; this term accounts for the of due to internal in the . A key application of the poise arises in modeling through circular pipes, described by the Hagen-Poiseuille equation. For steady, , the ΔP along a pipe of length L and r carrying Q is given by: ΔP=8ηLQπr4\Delta P = \frac{8 \eta L Q}{\pi r^4} This relation, derived from the Navier-Stokes equations under no-slip boundary conditions and axial symmetry, allows experimental determination of η by measuring ΔP, L, Q, and r in setups like capillary tubes. The poise also factors into the Reynolds number Re, a dimensionless quantity that predicts flow regimes: Re = ρ v D / η, where ρ is fluid density, v is , and D is a length scale such as pipe diameter. Low Re (typically < 2000) indicates dominated by , while high Re signals driven by inertia; calculations using η in poise require consistent CGS units for ρ (g/cm³), v (cm/s), and D (cm) to yield a unitless Re. In experimental , the poise enables viscosity measurements via falling viscometers based on , applicable for low-Re . For a of r and ρ falling at v through a of σ, the viscosity is: η=29(ρ−σ)gr2v\eta = \frac{2}{9} \frac{(\rho - \sigma) g r^2}{v} Here, η emerges in poise when using CGS units (g in cm/s², r in cm, v in cm/s), providing a direct method to characterize in simulations of particle-laden flows. Scientific contexts spanning physics and engineering often employ the poise for its alignment with CGS-based simulations. In , air's dynamic is approximately 0.00018 P at standard conditions, influencing development over surfaces. In , modeling molten rock flows in planetary mantles uses viscosities ranging from 10³ P for hot, low-silica magmas to over 10¹⁵ P for cooler, silica-rich ones, affecting patterns and .

In Rheology and Industry

In , the poise serves as a key unit for quantifying dynamic , particularly in the analysis of non-Newtonian fluids where viscosity depends on the applied , as seen in shear-thinning materials like paints that exhibit reduced resistance to flow under increasing shear. This variability allows rheologists to characterize complex flow behaviors essential for , with instruments such as Brookfield rotational viscometers commonly reporting measurements in poise or its submultiple, the centipoise (cP), to assess how fluids respond to deformation. Industrial applications of the poise span diverse sectors, including coatings where paints and inks typically exhibit viscosities ranging from 1 to 100 P to ensure proper application and drying without sagging or uneven spreading. In lubrication, oils for engines and machinery often fall in the 0.1 to 10 P range at operating temperatures, balancing strength and energy efficiency to minimize . Food processing similarly relies on the unit for products like syrups, which can reach 10 to 1000 P, influencing texture and pourability in items such as or . Quality control in leverages poise measurements to maintain consistent material flow, as in polymer where higher values—often exceeding 100 P in melts—indicate thicker formulations that prevent defects like die swell or uneven thickness. Rotational viscometers provide routine assessments in poise or cP for these processes, while methods offer precise for high-viscosity industrial standards, ensuring reproducibility across batches. Although the poise persists in legacy CGS-based industries like pharmaceuticals for formulating viscous suspensions and ointments, modern global standards increasingly convert values to pascal-seconds (Pa·s), where 1 P equals 0.1 Pa·s, to align with SI conventions.

References

  1. https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-5-units-outside-si
  2. https://hydramotion.com/uploads/view/20160224144736_Hydramotion_Viscosity_Units.pdf
  3. https://www.oxfordreference.com/display/10.1093/oi/authority.20110803100333690
  4. https://www.rheosense.com/basics/viscosity-units
  5. https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Physical_Methods_in_Chemistry_and_Nano_Science_%28Barron%29/02%253A_Physical_and_Thermal_Analysis/2.06%253A_Viscosity
  6. https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-8
  7. https://physics.info/viscosity/
  8. https://scienceworld.wolfram.com/physics/Poise.html
  9. https://www.calcsimpler.com/units-and-measures/the-poise-cgs-unit-of-dynamic-viscosity
  10. https://www.engineeringtoolbox.com/dynamic-absolute-kinematic-viscosity-d_412.html
  11. https://www.unitconverters.net/viscosity-dynamic/poise-to-pascal-second.htm
  12. http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/viscosity.html
  13. https://www.ibiblio.org/units/cgsmks.html
  14. https://hydramotion.com/en/technical/units-of-viscosity
  15. https://www.engineeringtoolbox.com/water-dynamic-kinematic-viscosity-d_596.html
  16. https://wiki.anton-paar.com/en/water/
  17. https://www.convertunits.com/info/millipoise
  18. https://www.convertunits.com/from/megapoise/to/poise
  19. https://pubmed.ncbi.nlm.nih.gov/779509/
  20. https://www.researchgate.net/publication/234151045_The_History_of_Poiseuille%27s_Law
  21. https://archive.org/details/BIUSante_TPAR1828x166
  22. https://depts.washington.edu/jrphys/ph115S13/Pois.pdf
  23. https://homepage.ntu.edu.tw/~wttsai/Adv_Fluid/Poiseuille%20and%20his%20law.pdf
  24. https://opg.optica.org/abstract.cfm?uri=josa-7-4-335
  25. https://nvlpubs.nist.gov/nistpubs/bulletin/14/nbsbulletinv14n1p59_a2b.pdf
  26. https://nvlpubs.nist.gov/nistpubs/nbstechnologic/nbstechnologicpaperT100.pdf
  27. https://www.britannica.com/science/stoke-physics
  28. http://www.damtp.cam.ac.uk/user/tong/fluids/fluids2.pdf
  29. https://mahi.ucsd.edu/guy/sio224/stokes-part2.pdf
  30. https://www.engineeringtoolbox.com/poiseulle-formula-d_1625.html
  31. https://phys.libretexts.org/Bookshelves/College_Physics/College_Physics_1e_%28OpenStax%29/12%253A_Fluid_Dynamics_and_Its_Biological_and_Medical_Applications/12.04%253A_Viscosity_and_Laminar_Flow_Poiseuilles_Law
  32. https://www.gigacalculator.com/calculators/reynolds-number-calculator.php
  33. https://resources.saylor.org/wwwresources/archived/site/wp-content/uploads/2011/04/Viscosity.pdf
  34. https://chem.libretexts.org/Courses/Montana_State_University/MSU%253A_CHMY_362_Elements_of_Physical_Chemistry/02%253A_Viscosity/2.02%253A_Viscosity_Theory
  35. https://www.engineersedge.com/physics/viscosity_of_air_dynamic_and_kinematic_14483.htm
  36. http://ui.adsabs.harvard.edu/abs/1985JVGR...24..193M/abstract
  37. https://www.sciencedirect.com/topics/earth-and-planetary-sciences/newtonian-fluid
  38. https://3819277.app.netsuite.com/core/media/media.nl?id=372800&c=3819277&h=6d930075efbea3a509c2&_xt=.pdf
  39. https://www.engineeringtoolbox.com/dynamic-viscosity-motor-oils-d_1759.html
  40. https://www.engineeringtoolbox.com/absolute-viscosity-foods-d_1827.html
  41. https://www.dynisco.com/userfiles/files/Practical_Rheology_Section_3.pdf
  42. https://www.tappi.org/content/events/07europlace/papers/07europl43.pdf
  43. https://www.linkedin.com/pulse/pharm-glass-properties-part-4-viscosity-matthew-hall
Add your contribution
Related Hubs
User Avatar
No comments yet.