1. Thermo-physical properties 2. Radiation properties - nptel - Indian ...

Mechanical Measurements Prof S.P.Venkatesan
Indian Institute of Technology Madras
Figure 21 Schematic of a rotating cylinder viscometer
The nomenclature used in the following derivation is given in Figure 21. If the
gap a between the two cylinders is very small compared to the radius of any of
the cylinders we may approximate the flow between the two cylinders to be
coquette flow familiar to us from fluid mechanics. The velocity distribution across
2
the gap a is linear and the constant velocity gradient is given by
r du ω
= . The
dr b
uniform shear stress acting on the surface of the inner cylinder all along its length
L is then given by
due to this is
r du ω
dr b
2
τ=μ =μ . The torque experienced by the inner cylinder
2
2
1 2
μωr 2πμωr r
TL = × 2π rL 1 × r1
=
b
b
Shear stress
Liquid
film
L
Surface area
Moment arm
Stationary
cylinder
Constant
rotational
speed ω
Rotating
cylinder
There is another contribution to the torque due to the shear stress at the bottom
of the cylinder due to the liquid film of thickness a. At a radial distance r from the
center of the stationary cylinder the shear stress is given by
a
r1
r2
b
(17)
ωr
τ=μ . Consider
a