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.
Want to see more full solutions like this?
Chapter 7 Solutions
Fluid Mechanics: Fundamentals and Applications
- According to the U.S. Geological survey, the volume of water in oceans, seas, and bays is 1.41 ✕ 1018 m3. The average concentration of naturally occurring uranium in seawater is 3.15 ✕ 10−6 kg/m3. If 0.670% of naturally occurring uranium is the fissionable isotope U-235 and each fission reaction yields 200 MeV, estimate the amount of time the uranium in the seawater on the planet could meet the planet's energy needs at an average usage of 1.94 ✕ 1013 J/s.arrow_forwardA hollow aluminum cylinder 16.5 cm deep has an internal capacity of 2.000 L at 23.0°C. It is completely filled with turpentine at 23.0°C. The turpentine and the aluminum cylinder are then slowly warmed together to 75.0°C. (The average linear expansion coefficient for aluminum is 2.4 10-5 °C−1, and the average volume expansion coefficient for turpentine is 9.0 10-4 °C−1.) How much turpentine overflows?arrow_forwardHow does the rate of heat transfer by conduction change when all spatial dimensions are doubled?arrow_forward
- Heat Transfer You are cooking asparagus for dinner. The asparagus is fried in oil at atemperature of 230 C. You then want to stop cooking so you dip it into an ice bath at 10 C. You can assume that the asparagus is a cylinder with L=25 cm and D=1 cm and has a conduction coefficient of k=1.6 W/m K. Your water bath is large, 1 m × 1 m × 1 m and you fully submerge you asparagus by 10 diameters. Find the shape factor, thermal resistance and heat transfer rate for this system.arrow_forwardA 3-meter - long steel pipe has its upper end leaning against a vertical wall and lower end on a level ground. The lower end moves away at a constant rate of 2 cm/s. How fast is the pipe rotating when the lower end is 2 meters from the wall in rad/sec?0.009840.008940.004890.00725arrow_forwardAn oven made of stone with 3 m length and semi-cylindrical shape losses heat from inlet section of the surface shell (ri = 50 cm) to outlet section (ro = 62 cm) by convection and radiation. According to the system conditions showing on the following figure; calculate Ti value if To temperature is 35 °C (Assume steady state and one dimensional condition and ε = 0,90; σ = 5,67x10-8 W/m2K4)arrow_forward
- prove that heat transfer is a path function?arrow_forwardThe candle flame is an example ofa. Open system, real and fixed boundaryb. open system, imaginary and variable boundaryc. Closed system, real and variable boundaryd. Closed system, imaginary and fixed boundaryarrow_forwardThis question related to engineering mechanics.arrow_forward
- Please solve both parts with handwriting please need with correct answer need awesome answer solve both handwriting i requested to u. Part6. An exposed 8 cm external diameter, 20 m long hot-water pipe at 80°C is losing heat to the surrounding (outdoor) air by natural convection. The average outdoor temperature is 5°C. The heat transfer coefficient is 25 W/m2°C. What is the heat loss by natural convection, in kW? A. 9.4 W B. 10.0 W C. 10.4 W D. 11.4 W Part7. A spherical ball with a diameter of 10 cm has an outer surface that is maintained at a temperature of 200°C. It is suspended in the middle of a room that has an average temperature of 20°C. If the surface emissivity is 0.8, determine the rate of radiative heat transfer from the ball to the room in W. (Choose the nearest value) A. 2.3 W B. 4.5 W C. 19.4 W D. 60.8 Warrow_forwardHeat transfer is a discipline of thermal engineering that concerns the generation, use, conversion,and exchange of thermal energy (heat) between physical systems. How do you connect it with thermodynamics and why is it necessary for us, mechanical engineers, to study it?arrow_forwardA model of a spring/mass system is 4x" + e-0.1tx = 0. Byinspection of the differential equation only, discuss the behaviorof the system over a long period of time.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning