GENERAL UNCERTAINTY ANALYSIS

ERDC TN-DOER-I5

August 2000

sediments (silts and clays) transported in large pipelines in fully turbulent flow are considered

non-settling (homogeneously distributed). Sand-sized sediments stratify in the pipeline depending

on particle size and concentration. A properly mounted density gauge is oriented at a 45-deg angle

from the horizontal to insure that a representative sediment concentration profile is sampled. The

larger the median grain size transported, the higher the degree of uncertainty in the density gauge

measurement. For coarse sediment transport, the uncertainty could be much higher.

Differential Pressure Transducers. The pressure transducers located on the bottom of the

hull of the vessel and used to measure the draft of the vessel because of the load in the hopper have

accuracies of about 1 percent of the range of measurement when used for dredging applications.

The actual calibrated accuracy of these transducers may be better than 1 percent, but additional error

is introduced because the draft of the vessel is influenced by other factors such as the amount of

fuel and ballast that the vessel is carrying, as well as the motion of the vessel caused by wave action.

Water Surface Elevation Transducers. The transducers designed to measure the surface of

the material in large dredge hoppers operate on either ultrasonic or microwave signal transmission

and reception principles. The accuracy of these transducers is estimated to be about 1 percent of the

range of measurement for dredging applications.

Measurement of the Diameter of the Dredge Pipe. There is some assumed error in the

measurement of the diameter of the discharge pipe on a dredge. Because there are many makes of

pipe used in dredging, an assumed error of 0.00025 m will be used for the following error analysis.

GENERAL UNCERTAINTY ANALYSIS: A general uncertainty analysis is a mathematical

method of determining how the error associated with each variable in a data reduction equation

(such as a production equation) propagate through the equation to the final calculated result. For

the case of the production calculation equations, the variables and their associated error are the water

density, sediment mineral density, in situ sediment density, slurry density in the pipeline, flow

velocity measurements, pipe diameter measurements, and average density in the hopper (pressure

transducer and water level transducer measurements).

A detailed description of the principles and theory of the general uncertainty analysis technique is

given by Coleman and Steel (1989). For the purpose of this document, only the basic uncertainty

analysis expression will be described along with a procedural method for solving the expression for

the desired result.

To demonstrate the general uncertainty analysis technique, the equation describing the in situ

volumetric flow rate production will be analyzed step-by-step using this method. Earlier in the

document, the equation for the volumetric flow rate of in situ materials measured by an in-line

production meter was defined as:

a fa f

ρ - ρw

VOL t = s

(5)

ρi - ρw