A device reduces particulate from \( 8.4 \) g/m\(^3\) to \( 0.21 \) g/m\(^3\). Its collection efficiency is
Answer: A
The efficiency is \( (8.4-0.21)/8.4 = 0.975 \). Efficiency figures alone can mislead, since a device at 97.5 per cent still passes a fifth of a gram per cubic metre, and it is the outlet concentration that a standard is written against.
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Two devices in series achieve \( 90 \) and \( 95 \) per cent efficiency. The overall efficiency is
Answer: B
The penetrations multiply, so \( 0.10 \times 0.05 = 0.005 \) passes and 99.5 per cent is collected. Working in penetration rather than efficiency is much the easier way to handle devices in series, and it makes the diminishing returns obvious.
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A settling chamber \( 6 \) m long and \( 2 \) m high passes gas at \( 0.6 \) m/s. The minimum settling velocity for complete collection is
Answer: C
Residence time is \( 6/0.6 = 10 \) s, and a particle must fall 2 m in that time, requiring \( 0.20 \) m/s. Settling velocities of that order belong to particles well above a hundred micrometres, which shows how limited the device is.
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Applying the Deutsch-Anderson equation with a migration velocity of \( 0.10 \) m/s, a plate area of \( 4000 \) m\(^2\) and a flow of \( 100 \) m\(^3\)/s gives an efficiency of
Answer: D
The exponent is \( -Aw/Q = -4000 \times 0.10/100 = -4 \), and \( 1 - e^{-4} = 0.982 \). Because the relationship is exponential, raising the efficiency to 99.5 per cent would require more than a third as much plate area again.
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To raise a precipitator from \( 98.2 \) to \( 99.5 \) per cent at the same flow and migration velocity, the plate area must rise from \( 4000 \) m\(^2\) to about
Answer: A
The exponent must move from 4 to \( -\ln 0.005 = 5.30 \), so the area rises in the same ratio to 5300 square metres. A third more steel for one and three tenths of a percentage point is the characteristic economics of precipitator design.
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A baghouse treats \( 30 \) m\(^3\)/s with \( 900 \) m\(^2\) of fabric. Its air to cloth ratio is
Answer: B
Correct answer: 0.033 m/s
The air to cloth ratio is gas flow over fabric area:
\[ \frac{30}{900} = 0.033 \ \mathrm{m/s} \]It has the units of a velocity and is often called the filtration velocity. Values around 0.01 to 0.02 m/s are usual for reverse air cleaning and 0.03 to 0.05 for pulse jet; too high a ratio drives dust into the fabric, raises the pressure drop and shortens bag life.
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A fan moves \( 40 \) m\(^3\)/s against a pressure drop of \( 9 \) kPa at \( 70 \) per cent efficiency. The power required is
Answer: C
Correct answer: 514 kW
Fan power is flow times pressure drop divided by efficiency:
\[ P = \frac{Q\Delta p}{\eta} = \frac{40 \times 9000}{0.7} = \frac{360\,000}{0.7} \approx 514 \ \mathrm{kW} \]Half a megawatt to move the gas is what a venturi scrubber’s high pressure drop costs, and over a year it dominates the whole economics of the installation. Multiplying by the efficiency instead of dividing gives 252 kW and would have the fan produce more than it consumed.
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A cyclone has a cut diameter of \( 12 \) micrometres. Halving the body diameter, with efficiency scaling as the square root of the body diameter, gives a cut diameter of about
Answer: D
The cut diameter falls by \( \sqrt{0.5} = 0.707 \), giving \( 12 \times 0.707 = 8.5 \) micrometres. The pressure drop rises steeply at the same time, which is the standing trade in cyclone design and the reason multiclones exist.
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A wet scrubber uses \( 1.2 \) litres of liquid per cubic metre of gas at \( 25 \) m\(^3\)/s. The liquid rate is
Answer: A
Correct answer: 30 litres per second
The liquid rate is the specific consumption times the gas flow:
\[ 1.2 \times 25 = 30 \ \mathrm{litres/s} \]Around one to two litres per cubic metre is typical of a venturi. That liquid must then be recirculated, and the solids it has picked up removed, which is the effluent handling that goes with every wet device.
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A precipitator passes \( 0.4 \) per cent of the inlet dust. Its efficiency is
Answer: B
Efficiency is one minus the penetration, so \( 1 - 0.004 = 0.996 \). Quoting penetration rather than efficiency makes the comparison between good devices far clearer, since 99.6 and 99.8 per cent differ by a factor of two in what escapes.
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