Question

A thin oil film .003 inches thick separates two plates. The moving plate is 4 inches on each side. It takes 4lbs of force to move the top plate at a constant velocity of 4ft/s. What is the dynamic viscosity of the oil in Cp?

Answer 1

Dynamic viscosity is the resistance to movement of one layer of a fluid over another.

Shear stress can be expressed

τ = μ dc / dy  

τ = μ γ      (1)

where

τ = shearing stress in fluid (N/m²)

μ = dynamic viscosity of fluid (N s/m²)

dc = unit velocity (m/s)

dy = unit distance between layers (m)

γ = dc / dy = shear rate (s^-1)

Equation (1) is known as the Newtons Law of Friction.

Equation (1) can be rearranged to express Dynamic viscosity as

   μ = τ dy / dc

μ = τ  / γ      (2)

The basic units of dynamic viscosity are Poise(poise), Centipoise(cP), lbm/ft/s, or Pa×s. The relationship between various units is given in Table 4.1.

Table 4.1. Relationship between viscosity units

	Poise	cP	lbm/ft/s	Pa×s
poise	1	0.001	0.0672	0.1
cP	100	1	0.000672	0.001
lbm/ft/s	14.88	1488	1	1.488
Pa×s	10	1000	0.672	1

From the given question data,

Dynamic Viscosity,     μ = τ dy / dc

Where             τ = 4lbs,

dy = 0.003inch

dc = 4ft/s

We know that 1 inch = 0.0833 ft

Thus, 0.003 inch = 0.00025 ft

                          μ = 0.00025 lbs

from above table 4.1, 1 lbs = 1488 cP

            Therefore, μ = 0.00025 * 1488

                        μ =0.372cP