DEUTSCH-ANDERSON EQUATION

F = 1- e^-wA/Q.............................................................................(8)

F = fraction collected

Q = Flow rate of gas m³/s

w = effective drift velocity m/s , the terminal speed of particle as it strikes the plate.

This is an empirical relationship.

w - must be determined through pilot plant studies for a particular effluent stream or we can gain information from previous experience of smaller systems of the same type.

WORKED EXAMPLE.

An electrostatic precipitator with 6000m² of collector plates is 97% efficient when collecting particles from a plant which has a volumetric emission rate of 200m³/s.

1. What is the terminal velocity of the particles collected from the gas stream?
2. What plate area , of the same precipitator design would ensure a 98% efficiency?
3. What would the efficiency be if we increased the area to 10000m³?

START BY REARRANGING THE FORMULA:

F = 1- e^-wA/Q

-1+F=-e^-wA/Q

1-F=e^-wA/Q

ln(1-F)=^-wA/Q

(-ln(1-F)) = wA/Q

Q/A(-ln(1-F))=w

(-Q/A)(ln(1-F))=w

ALSO

THUS

1. w=(-200m³/s/6000m²)(ln(1-0.97)

   w=(-1/30m/s)((ln(1-0.97))

   w=0.117m/s

2. At 98%

   A=(-200m³/s/0.117m/s)(ln(1-0.98)

   A=6687 m²

3. F = 1- e^-wA/Q

   F=1- exp -(0.117m/s x 10000m²/200m³/s)

   F=1-exp-(5.85)

   F=.997

   % Efficiency = 99.7%