Editing Viscometer (section)

==Standard laboratory viscometers for liquids==
[[File:Ostwaldscher Zähigkeitsmesser.jpg|thumb|right|100px|Ostwald viscometers measure the viscosity of a fluid with a known density.]]

===U-tube viscometers===
These devices are also known as glass capillary viscometers or '''Ostwald viscometers''', named after [[Wilhelm Ostwald]]. Another version is the [[Ubbelohde viscometer]], which consists of a U-shaped glass tube held vertically in a controlled temperature bath. In one arm of the U is a vertical section of precise narrow bore (the capillary). Above there is a bulb, with it is another bulb lower down on the other arm. In use, liquid is drawn into the upper bulb by suction, then allowed to flow down through the capillary into the lower bulb. Two marks (one above and one below the upper bulb) indicate a known volume. The time taken for the level of the liquid to pass between these marks is proportional to the kinematic viscosity. The calibration can be done using a fluid of known properties. Most commercial units are provided with a conversion factor.

The time required for the test liquid to flow through a capillary of a known diameter of a certain factor between two marked points is measured. By multiplying the time taken by the factor of the viscometer, the kinematic viscosity is obtained.

Such viscometers can be classified as direct-flow or reverse-flow. Reverse-flow viscometers have the reservoir above the markings, and direct-flow are those with the reservoir below the markings. Such classifications exist so that the level can be determined even when opaque or staining liquids are measured, otherwise the liquid will cover the markings and make it impossible to gauge the time the level passes the mark. This also allows the viscometer to have more than 1 set of marks to allow {{clarify span|for an immediate timing of the time it takes to reach the 3rd mark|date=January 2019}}, therefore yielding 2 timings and allowing subsequent calculation of determinability to ensure accurate results. The use of two timings in one viscometer in a single run is only possible if the sample being measured has [[Newtonian fluid|Newtonian properties]]. Otherwise the change in driving head, which in turn changes the shear rate, will produce a different viscosity for the two bulbs.

===Falling-sphere viscometers===
[[File:Terminal velocity.svg|thumb|100px|right|Creeping flow past a sphere]]
[[Stokes' law]] is the basis of the falling-sphere viscometer, in which the fluid is stationary in a vertical glass tube. A sphere of known size and density is allowed to descend through the liquid. If correctly selected, it reaches [[terminal velocity]], which can be measured by the time it takes to pass two marks on the tube. Electronic sensing can be used for opaque fluids. Knowing the terminal velocity, the size and density of the sphere, and the [[density]] of the liquid, Stokes' law can be used to calculate the [[viscosity]] of the fluid. A series of steel ball bearings of different diameter are normally used in the classic experiment to improve the accuracy of the calculation. The school experiment uses [[glycerol]] as the fluid, and the technique is used industrially to check the viscosity of fluids used in processes. It includes many different oils and [[polymer]] liquids {{clarify span|such as solutions|date=January 2019}}.

In 1851, [[George Gabriel Stokes]] derived an expression for the frictional force (also called [[drag force]]) exerted on spherical objects with very small [[Reynolds number]]s (e.g., very small particles) in a continuous [[viscosity|viscous]] [[fluid]] by changing the small fluid-mass limit of the generally unsolvable [[Navier–Stokes equations]]:

: <math>F = 6 \pi r \eta v,</math>

where
: ''<math>F</math>'' is the frictional force,
: ''<math>r</math>'' is the radius of the spherical object,
: ''<math>\eta</math>'' is the fluid viscosity,
: ''<math>v</math>'' is the particle velocity.

If the particles are falling in the viscous fluid by their own weight, then a terminal velocity, also known as the settling velocity, is reached when this frictional force combined with the [[buoyant force]] exactly balance the [[gravitational force]]. The resulting settling velocity (or [[terminal velocity]]) is given by

: <math>V_\text{s} = \frac{2}{9} \frac{r^2 g (\rho_p - \rho_f)}{\mu},</math>

where:
: {{math|''V''<sub>s</sub>}} is the particle settling velocity (m/s), vertically downwards if {{math|''ρ''<sub>p</sub> &gt; ''ρ''<sub>f</sub>}}, upwards if {{math|''ρ''<sub>p</sub> &lt; ''ρ''<sub>f</sub>}},
: {{mvar|r}} is the [[Stokes radius]] of the particle (m),
: {{mvar|g}} is the [[gravitational acceleration]] (m/s<sup>2</sup>),
: {{math|''ρ''<sub>p</sub>}} is the [[density]] of the particles (kg/m<sup>3</sup>),
: {{math|''ρ''<sub>f</sub>}} is the [[density]] of the fluid (kg/m<sup>3</sup>),
: {{mvar|μ}} is the (dynamic) fluid [[viscosity]] (Pa·s).

Note that [[Stokes flow]] is assumed, so the [[Reynolds number]] must be small.

A limiting factor on the validity of this result is the [[surface roughness|roughness]] of the sphere being used.

A modification of the straight falling-sphere viscometer is a rolling-ball viscometer, which times a ball rolling down a slope whilst immersed in the test fluid. This can be further improved by using a patented V plate, which increases the number of rotations to distance traveled, allowing smaller, more portable devices. The controlled rolling motion of the ball avoids turbulences in the fluid, which would otherwise occur with a falling ball.<ref>{{Cite web|last=tec-science|date=2020-04-04|title=Experimental determination of viscosity (viscometer)|url=https://www.tec-science.com/mechanics/gases-and-liquids/experimental-determination-of-viscosity/|access-date=2020-06-25|website=tec-science|language=en-US}}</ref> This type of device is also suitable for ship board use.{{why?|date=January 2019}}