Page 100 - Modelling in Transport Phenomena A Conceptual Approach

80 CHAPTER 4. EVALUATION OF TRANSFER COEFFICIENTS

H Calculate p; given Dp and vt
In this case Eq. (4.3-4) must be rearranged so that the fluid viscosity can be
eliminated. If both sides of Eq. (4.3-4) are divided by Re:, the result is

f=X (4.3-20)
where X, which is independent of p, is a dimensionless number defined by

(4.3-21)

Substitution of Ekl. (4.3-10) into Eq. (4.3-20) gives
X=- 24 (1 + 0.173 Re$657) + 0.413 (4.3-22)
Rep 1 + 16,300

Since Eq. (4.3-22) expresses X as a function of the Reynolds number, calculation
of the fluid viscosity for a given terminal velocity and particle diameter requires
an iterative solution. To circumvent this problem, the following explicit expression
relating X to the Reynolds number is proposed by Tosun and Akgahin (1992) as

(4.3-23)

The procedure to calculate the fluid viscosity is as follows:

a) Calculate X from Eq. (4.3-21),
b) Substitute X into Eq. (4.3-23) and determine the Reynolds number,
c) Once the Reynolds number is determined, the fluid viscosity can be calculated
from the equation
(4.3-24)

Example 4.6 One way of measuring fluid viscosity is to use a falling ball viscome-
ter in which a spherical ball of known density is dropped into a fluid-filled graduated
cylinder and the time of fall for the ball for a specified distance is recorded.
A spherical ball, 5mm in diameter, has a density of 1000kg/m3. It falls
through a liquid of density 910kg/m3 at 25°C and travels a distance of lOcm
in 1.8min. Determine the viscosity of the liquid.

Solution
The terminal velocity of the sphere is
Distance
ut =
Time