Question

A concentric cylinder viscometer may be formed by rotating the inner member of a pair of closely fitting cylinders (see Fig). The annular gap is small so that a linear velocity profile will exist in the liquid sample. Consider a viscometer with an inner cylinder of 4 in. diameter and 8 in. height, and a clearance gap width of 0.001 in., filled with castor oil at 90°F. Determine the torque required to turn the inner cylinder at 400 rpm.

Answer 1

Answer:

T = 52.76 ft . lbf

Explanation:

Given data:

inner diameter of cylinder 4 in

height of cylinder 8 in

gap width = 0.001 in

we know shear force is given as

$F =\tau A = \tau (2\pi RH)$

Where, $\tau$ is torque acting on cylinder

$\tau = \mu \frac{V}{d} = \mu \frac{ R\omega}{d}$

$\mu$ is kinematic viscosity, for castor oil at 90 degree F  = 0.259 N s/m^2

substituing all value in   shear force formula we get

$F = \frac{2\pi \mu R^2\omega h}{d}$

we know that

$Torque, T = force \times R$

$T = \frac{2\pi \mu R^3\omega h}{d}$

$T = \frac{2\pi (0.259\times 2.09\times 10^{-2}\times 2^3\times 400\times 8 }{10^{-3}} \times 2\pi \times \frac{1 min}{60} \times \frac{1 ft^3 }{1728 in^3}$

T = 52.76 ft . lbf