Summary of Research on Viscosity

What is viscosity?

Viscosity is a measure of the resistance of a liquid to flow.

Viscosity (represented by the symbol η) is the ratio of the shear stress (F/A) to the velocity gradient (Δv_x/Δz or dv_x/dz) in a fluid.

η =

⎛ ⎝

F

⎞ ⎠

÷

⎛ ⎝

Δvx

⎞ ⎠

or

η =

⎛ ⎝

F

⎞ ⎠

÷

⎛ ⎝

dvx

⎞ ⎠

A

Δz

A

dz

F = Force applied

A = Cross-sectional area of material perpendicular to the force applied

v = velocity

z = distance

What is kinematic viscosity?

Kinematic viscosity is when viscosity is measured by timing the flow of a fixed volume of liquid from a viscosity measuring cup. (Zahn cups) The SI Unit for kinematic viscosity is Centistokes (cSt).

What are Zahn Cups?

Zahn cups are cups used to measure kinematic viscosity of liquids. They are 5 types of Zahn Cups, meant for different range of viscosities. They differ only in the size of the orifice (hole).

Catalog No.	Cup No.	Orifice, inch	Liquid type	Zahn range, seconds (250°C)	Range, Centistokes
3410-01	1	0.078	Very thin	45-80	18-56
3401-02	2	0.108	Thin	25-80	40-230
3401-03	3	0.148	Medium	20-75	150-790
3401-04	4	0.168	Heavy-thick	20-80	220-1100
3401-05	5	0.208	Very heavy-thick	20-75	460-1725+

In my experiment, I will most probably only be making use of Zahn Cup #1 as I only need to measure viscosities of up to 30. Zahn cups measure viscosity by measuring the time taken for 44ml of liquid to flow from the cups.

GENERAL FORMULA

V= K (T – C)

where: V is Kinematic Viscosity (cSt)

T is Efflux time (Zahn seconds)

K + C are constants ( Ref. # 1)

SPECIFIC FORMULAS

Zahn cup # Formula “T range seconds”

1 V = 1.1 ( T-29) 45-80

2 V = 3.5 (T-14) 25-80

3 V= 11.7 (T-7.5) 20-75

4 V= 14.8 (T-5) 20-80

5 V= 23 (T-0) 20-75

What is drag?

Drag, in fluid dynamics, refers to forces that oppose the relative motion of an object through a fluid (a liquid or gas). Drag forces depend on velocity.

STOKE'S GREAT LAW OF DRAG

If

r = the radius of a sphere in cm
d₁ = the density of the sphere in g/cm³
d₂ = the density of the fluid in g/cm³
g = the local gravitational acceleration in cm/S²
c = the Viscosity of the fluid in Poise
v = the terminal velocity in cm/S

Then

From this, I can derive that the more viscous the fluid, the smaller the terminal velocity. Thus, I can form an hypothesis for my experiment (how does viscosity affect the movement of a pendulum in terms of speed?): The higher the viscosity of the liquid, the slower the pendulum will travel, therefore, the longer the time taken for one oscillation.