SME
Environmental Engineering · Problem type
Control devices in series
Use this for “A cyclone catches 90% of the dust and a scrubber after it catches 80% of the rest. Find the overall efficiency.”
Chart
This is an example. Type your own values to start a new problem.
η (%)
=
100
%
−
(100
%
−
η₁ (%)
)
×
(100
%
−
η₂ (%)
)
P₁
Through device 1
worked out (not typed) · %
P₂
Through both
worked out (not typed) · %
Formulas
P₁
=
100
−
η₁
10 = 100 − 90
P₂
=
P₁
×
100 −
η₂
100
2
=
10
×
100 − 80
100
η
=
100
−
P₂
98 = 100 − 2
Assumptions
•
Each efficiency is by mass of the dust reaching that device; device 2 sees only what device 1 passes.
•
η₂ is measured on the dust leaving device 1, which is finer than the dust that entered.
•
η = 1 − (1 − η₁)(1 − η₂), worked here in percent through what each device lets through.
Step-by-step
WE KNOW
η₁ = 90%, η₂ = 80%
FIND
through device 1 (P₁), through both (P₂), overall efficiency (η)
Step 1 · Find through device 1 (P₁)
Use P₁ = 100 − η₁
What device 1 does not catch passes on.
P₁
=
100
−
90
P₁
=
10%
Step 2 · Find through both (P₂)
Use P₂ = P₁ × (100 − η₂) ÷ 100
Device
2
lets
through
100
−
η₂
percent
of
the
dust
that
reaches
it.
P₂
=
10
×
100 − 80
100
P₂
=
10
×
20
100
P₂
=
200
100
P₂
=
2%
Step 3 · Find overall efficiency (η)
Use η = 100 − P₂
Only what leaves the last device escapes; the rest is caught.
η
=
100
−
2
η
=
98%
Check
Put the numbers back in. Both sides should match.
10 = 100 − 90 ✓
2
=
10
×
100 − 80
100
✓
98 = 100 − 2 ✓
Topic check
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