A plate of area "A" moving under the action of a force "F" with a resulting velocity "V" over a fixed plate separated by a film of fluid "h" thick.   The shear stress on the fluid is "F / A".    For a Newtonian fluid the shear stress is directly proportional to the velocity gradient in the fluid- "dV /dh" .

P / A = m . dV /dy

The proportionality constant " m " is the viscosity and has units of ( N/m ²) .( m ). ( m / s ) = N . s / m ²...

The coherent SI unit of dynamic viscosity is the pascal second (Pa s).   This equates to a Newton second per square metre (N.s / m ² ).  In the cgs unit the poise is the corresponding unit which has dimensions of dyne seconds per cm ².   The centipoise (cP = 10 ^-2 poise) is the most common unit used in tables and handbooks.... 1 Pas = 1000. cP.   The viscosity of water at room temperature is approximately 1 cP

This is the ratio of the dynamic viscosity and the fluid density r ( kg /cubic m )  The SI unit of kinematic viscosity is the m ² / s.   The equivalent cgs unit is the stoke (St) which has the unit of cm ² / s.  The unit commonly used is the centistoke(cSt)....... 1 m ² / s = 10 ⁶ cSt

Absolute Kinematic Viscosity (m ² / s ) = m ( Pa s ) / r (kg / m³ )

Kinematic viscosity (centiStokes) = m (centiPoise) / r ( grammes /cubic cm )
For water with a density of about 1000kg/m³ the conversion is simply 1 cST = 1 cP

Viscosity conversion table Viscosity conversion table

A method of determining a lubrication fluids viscosity is to measure the rate of flow of the fluid through a test device.  The rate is measured in seconds the greater the number of seconds the more viscous the fluid.  This viscosity is seconds t = Saybolt universal Viscosity - seconds. The dynamic viscosity relates to the Saybolt universal viscosity (t) by the following formula

Viscosity m (Poise) = (0.00022 .t — 0.18 / t )

SAE (Society of automobile engineers ) has allocated numbers for specifying the viscosity of Engine Oils..

The SAE grades 0W through 25W, where W stands for Winter, have a maximum viscosity specified at low temperatures (—5 through —35�C), to ensure easy starting under low temperature conditions, and a minimum viscosity requirement at 100�C to ensure satisfactory lubrication at the final operating temperature.   The SAE grades 20 through 60 only have limits set at 100�C as these grades are not intended for use under low temperature conditions.

For marine applications, monograde oils of SAE 30 or SAE 40 are used because of the steady operating conditions in a ship's engine room.

On the other hand, automotive oils are normally formulated with Viscosity Index Improvers (VI Improvers) to provide multigrade performance.    VI Improvers are very large molecules, which are chemically made by linking together smaller molecules in a process called polymerization.   The resulting products, called polymers, may have molecular weights 1000 times or more greater than the base stock molecules.    The use of these special polymers makes it possible to meet both the low temperature viscosity requirements of the W grades as well as the high temperature requirements of the non-W grades.  Thus a SAE 20W 40 has the low temperature viscosity value of a SAE 20W oil at low temperatures and the high temperature viscosity of a SAE 40 oil at the higher temperature.

Different tests are completed to establish the viscosities for different operating regimes.   Tests are completed for low temperature

The ISO 3448 grading system for Industrial Engine Oils simply relates to the midpoint viscosity of oil in cStokes ( at 40^odeg ) as shown in the table below.

Kinematic viscosity (cST) = Dynamic Viscosity (cP)) / [1000.Density (kg/m³) ]

Table below is based on fluid with a sg = 1 (1000kg/m³)