GENERAL UNCERTAINTY ANALYSIS (cont.)

ERDC TN-DOER-I5

August 2000

The production equations for the solid and in situ volume hopper loads will involve an additional

uncertainty analysis. Note that in these expressions, the average density measured in the hopper,

(ρh), is a function of two measured variables, which are the weight of the material in the hopper as

measured by the vessel draft transducers and the volume of the material in the hopper as measured

by the water level transducers positioned over the hopper. Because of the dependence of the average

density of the material in the hopper on the two measured variables, a separate uncertainty analysis

must be performed on the following average density equation:

ρ=

(10)

VOLh

with Wh the weight of material in the hopper, and VOLh the measured volume in the hopper. The

result of this analysis will be used in finding the uncertainty of ρh for input into the final uncertainty

analysis expression for the hopper production calculations.

Substituting Equation 10 into Equation 3 results in the following expression for the in situ volume

load:

Wh - ρw VOLh

VOL =

(11)

ρi - ρw

with the hopper solids load defined as:

Wh - ρw VOLh

ρm

(12)

ρm - ρw

Applying the uncertainty analysis procedures to the previous production equations results in the

uncertainty expressions for hopper loads. The in situ volume uncertainty relationship is represented

by:

LMF ρh I F Uw I 2 + F -ρw I F Uv I 2

GH ρh - ρw JK GH Wh JK GH ρh - ρw JK GH Vh JK

UVOL

VOL

(13)

Up I 2 F Up I 2 O

JK + GH ρi - ρw JK PP

H ρi - ρw ρh - ρw