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TECHNICAL PAPERS

# Improving Falling Ball Tests for Viscosity Determination

[+] Author and Article Information
Shihai Feng1

Los Alamos National Laboratory, Los Alamos, NM 87545sfeng@lanl.gov

Alan L. Graham, Patrick T. Reardon

Los Alamos National Laboratory, Los Alamos, NM 87545

James Abbott

High Performance Computing Center, Texas Tech University, Lubbock, TX 79409

Lisa Mondy

Sandia National Laboratories, Albuquerque, NM 87185-0834

1

Corresponding author.

J. Fluids Eng 128(1), 157-163 (Aug 11, 2005) (7 pages) doi:10.1115/1.2137345 History: Received February 24, 2005; Revised August 11, 2005

## Abstract

Laboratory experiments and numerical simulations are performed to determine the accuracy and reproducibility of the falling-ball test for viscosity determination in Newtonian fluids. The results explore the wall and end effects of the containing cylinder and other possible sources that affect the accuracy and reproducibility of the falling ball tests. A formal error analysis of the falling-ball method, an evaluation of the relative merits of calibration and individual measurements, and an analysis of reproducibility in the falling-ball test are performed. Recommendations based on this study for improving both the accuracy and reproducibility of the falling-ball test are presented.

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## Figures

Figure 1

A three-dimensional BEM mesh of a spherical ball in a tube. Note the vertical wall mesh has been cut in half in order to view the ball clearly.

Figure 2

Falling balls reach terminal velocity in Newtonian fluids when the gap between the falling ball and the ends of the tube is greater than the tube radius. Here H is the gap between the falling ball and the surfaces of the fluid, and vt is the terminal velocity. Included are data from Tanner (17) and Graham (14).

Figure 3

The falling-ball velocity, v, of the ball when falling off-center normalized by the velocity of the ball falling along the centerline, vc, as a function of the dimensionless eccentricity. Note a∕R=0.1 in this figure.

Figure 4

Maximum increased falling-ball velocity as a function of the ratio of ball radius, a, to tube radius, R. Here vmax is the maximum falling-ball velocity for different sized balls when falling off-center.

Figure 5

Numerically simulated vertical settling velocity of the falling ball plotted against the distance between the center of the falling ball to the top surface of the fluid, Z, for the specific cases when the tube is tilted at 3° and a∕R=0.3. Data are shown for the measurement zone chosen as 4R from the top surface and 3.5R from the bottom of the cylinder.

Figure 6

Numerically simulated normalized time for the falling ball to pass through the timing zone chosen as 5R from the top surface and 4R from the bottom of the cylinder plotted against the tilt angle of the tube. Results are for a∕R=0.3.

Figure 7

Variability in 95% percent confident limit decreases as the number of trials increases.

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