1. Unit Operation Lab K S Chou Ch E, N T H U 1

2. A: Fluid Flow Experiments A1 - Friction Coefficient in Tubes A2 - Flowmeters  Types of flowing fluid: gas, liquid, solid, bubbled liquid, slurry, gas-solid (fluidization), solid-liquid-gas system;  Fluid flow: transportation  friction coefficient, viscosity, pressure drop, power required for transportation, choice of pumps, choice of tubes; 2

3. 3  Fermentation reactor: one example of solid- liquid-gas system

4. Friction Coefficient  Bernoulli eq. (incompressible fluid, steady state condition)  Pa/  + g Za/gc +  a Va2/2gc = Pb/  + g Zb/gc +  b Vb2/gc + hf  pressure energy + potential energy + kinetic energy + frictional loss = total energy  simplest case: pressure drop = frictional loss  (Pa – Pb)/ρ = hf 4

5.  fD = 4 fF = 4 Fw/(A K) where fD = Darcy’s friction factor; fF = Fanning friction factor; Fw = friction force; A = area of flow; K = kinetic energy/vol;  Taking circular tube as example: fF = (-ΔP g D) / (2 ΔL ρV2)…. Get data on the right hand side to calculate friction factor  In general: f = f(e/D, Re) e = surface roughness of tube wall; Re = d u ρ/  ; changes in both velocity and viscosity would change Re  For laminar flow: fD = 4 fF = 64/Re  For turbulent flow: (depending on smoothness of tube) ex. smooth tube 1/√fF = 4.06 log (Re √fF) + 2.16 5

6.  For sudden or gradual change in diameter: (expansion/ contraction): vortex formation cause energy loss  One special example: hf = Ke Va2/2gc, with Ke = (1- Aa/Ab)2; e: expansion 6

7.  fittings: splits, bend, elbow, U-tube, flanges, valves, etc  different loss due to different designs  empirical correlations are used mostly  General expression hf = Kf Va2/2 gc, with Kf as an empirical friction coefficient  Total friction loss = friction in straight tube + due to contraction + due to expansion + due to various fittings for this experiment 7

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10. 10 Various Flowmeters  orifice meter, Venturi meter, rotameter, etc.  discharge coefficient = f(Re); for orifice meter: Vo = Co √(2 gc  P/  ) 圖 A2-2 銳孔流量計之流出係數與 Re 關係。 其測 壓點屬 corner tap

11. 11 Venturi flowmeter and its discharge coefficient Vo= Cv/√(1-  4) √(2 g (ΔP/  )  = (d/D)

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13. 13 Pictures from Google to show different design of rotameter

14. 14 Other Types of Flowmeters  Magnetic flowmeter: used for dirty fluids or slurry, such as waste water; no moving part; based on Faraday principle: voltage generated E ~ V * B (magnetic field strength) * D (length of conductor) Taken from: Omega Engineering Technical Reference

15. 15 Ultrasonic Flow Meter  non-invasive; two types: Doppler type (frequency shift ~ velocity) and transit time type (  t ~ velocity)  taken from Flow meter directory