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CHEE 481 (2)

# Review notes I.doc

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School
Department
Chemical Engineering
Course
CHEE 481
Professor
Edward W Grandmaison
Semester
Winter

Description
CHEE 481 – Review Notes 1. PARTICLE SIZING: Normal distribution: 2 f x = 1 exp - (x - μ)  σ 2 π  2 σ2    1 z  x - μ )  1 1 F(z )= ∫ exp - 2  dx = + erc z 2 ) σ 2 π -∞  2 σ  2 2 Log-normal distribution: 1  (ln x - ln μ))2  f(x )= exp - 2  ln(σ ) 2 π  2 ln σ) ]  z 1  (ln x - ln μ ))2 1 1 F z = ∫ exp - 2  dx = + erc z 2 ) ln(σ ) 2 π -∞  2 [ln(σ )]  2 2 2. FLUID-PARTICLE FORCES: Terminal velocity for particles in gases: 2 g dp ρp Stokes law: U t 18 μ , K < 3.3 f g0.71 dp.14 ρp.71 Intermediate law: U t 0.153 0.43 0.29 , 3.3 < K < 43.6 μ f ρ f 1 / 2  g dpρ p Newton’s law: U =t1.74  ρ  , K > 43.6  f  3. DYNAMIC BALANCES – FLUID PARTICLE SYSTEMS: General formulation: m d U p = F p d t ∑ i m d U p = 3 π μfd p U - U )+ m f, where f is a force term (e.g. gravity) p d t K m f p p 2 d U p d p Kp m τ + U p = U f τ f, where τ = d t 18 μ f For changes in fluid velocity (U )f d U τ p + U p U f d t Step changes in U fead to exponential changes in U . p 4. STACK SAMPLING: Sampling locations in round ducts:  i 1 / 2 R i N  R    2i -11 / 2 ri=   R  2 N  Gas density - ideal gas law usually applies: n P ρ = = V R T 5. GRAVITY SETTLING CHAMBERS: • Collection efficiency is generally poor except for large particles, but very versatile and useful as a pre-treatment method for more sophisticated techniques. No mixing-plug flow model: L U t η = H U f Vertical mixing-plug flow model:   η =1 - exp - L U t  H U f where L = settling chamber length H = settling chamber height U = gas velocity through settling chamber f U t terminal velocity for particle These relations can be used to design for a suitable L/H ratio. With chamber dimensions, L, H and W (where W is the chamber width), Settling chamber “area” = A = WL Gas flow rate = Q = U H W L U t A ∴ = U t H U f Q This relationship can be used to design for an area A. 6. CYCLONES: • Better collection efficiency than GSC • Models more difficult to develop for practical design • For a “conventional” cyclone design, performance is known 1/2  9 μfW  Cut diamet
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