Water flows through tubes in a fluidized$-$bed combustor, where it is converted to steam.

The bed of the combustor consists of sorbent particles, which are used to absorb pollutants

given off during combustion. The particles are suspended in the combustor by a gas flowing

up from the bottom of the particle bed. The problem under investigation concerns the

corrosion effects of the exterior surface of the tubes used to carry the water through the

pipes. The following factors may influence the corrosion effects:

Factor

Bed temperature $(C)$

Tube temperature below the bed temp $(C)$

Particle size $(m)$

Environment

Particle material

Tube material

Levels

$700,1000$

$0,200,400$

$1000,3000,4000$

Oxidizing, sulfidizing

Limestone, dolomite

Stainless steel, iron

$($a$)$ Calculate the number of test runs needed for all possible combinations of the factor

levels to be included in the experiment.

$($b$)$ How many of these test runs are used in calculating the average corrosion

measurements for each of the above factor levels? For example, how many are used

when Bed temperature is at its low level? At its high level? How about the rest of

the factors?

$($c$)$ Suppose each factor was investigated on a separate experiment using the same

number of test runs just computed in $($b$)$ for each level. What would the total

experiment size be for separate investigations of each factor?