An electrostatic precipitator (ESP) is a device used in various applications to clean particle-laden air. First, the dusty air passes through the charging stage of the ESP. where dust particles are given a positive charge qp(coulombs) by charged ionizer wires (Fig. P7-118). The dusty air then enters the collector stage of the device, where it flows between two oppositely charged plates. The applied electric field strength between the plates is Ef(voltage difference per unit distance). Shown in Fig. P7-118 is a charged dust particle of diameter Dp. It is attracted to the negatively charged plate and moves toward that plate at a speed called the drift velocity w. If the plates are long enough, the dust panicle impacts the negatively charged plate and adheres to it. Clean air exits the device. It turns out that for very small particle the drift velocity depends only on qp. Ef,Dp, and air viscosity
(a)
The dimensionless relationship between the drift velocity through the collector stage of the ESP and the given parameters.
Answer to Problem 118P
The relationship between drift velocity and other parameter is
Explanation of Solution
Given:
Concept Used:
Buckinghams Pi Theorem
Calculation:
The electrostatic precipitalor is used to clean the air. Drift velocity of dust particle depends on qp, Ef, Dpand
There are 5 parameters, n=5
W is a function of
The primary dimension of each term
No. of primary dimensions are, j=4 (M, l, T, I)
No. of expected Pi = k= n-j =1
As j=4 we have to select four repeating parameters.
They are,
Combining repeating parameter with remaining parameters.
Now, dependent
The primary dimensions of the above term are
Equation becomes
Equating each primary dimension to solve
Current:
Mass:
Time:
Length:
Putting values in
Conclusion:
Thus, by using Buckinghams Pi theorem, we can develop the dimensionless relationship between drift velocity and other parameters.
(b)
The factor by which the drift velocity will change if the electric field strength is doubled.
Answer to Problem 118P
Drift velocity will be double if electric field strength is doubled.
Explanation of Solution
Given:
Electric field strength =Ef
Concept Used:
Where,
Calculation:
We have, the relation between drift velocity and another parameter as follows
Where,
Hence,
If electric is strength is doubled,
Conclusion:
Thus, drift velocity will be doubled if electric strength is doubled.
(c)
The factor by which the drift velocity will change for a given ESP if the particle diameter is doubled.
Answer to Problem 118P
Drift velocity will get half when particle diameter is doubled.
Explanation of Solution
Given:
Particle diameter −D
Concept Used:
Where,
Calculation:
We have relation between drift velocity and other parameter as follows:
Where,
Hence,
If particle diameter is doubled,
Conclusion:
Thus particle diameter is inversely proportional to drift velocity. Then drift velocity will get half when particle diameter is doubled.
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