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Unit Operation Lab

K S ChouCh E, N T H U

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A: Fluid Flow Experiments A1 - Friction Coefficient in TubesA2 - Flowmeters

Types of flowing fluid: gas (natural gas), liquid (tap water), 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;

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Fermentation reactor: one example of solid-liquid-gas system

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water

Storagetank

pump

Buffertank

PI

PT ( 壓力計)

90º elbow Straight pipe

PT (壓力計接頭)

180º elbow

Globe valve

Orifice meter

45º elbow

flange Venturi meter

Ballvalve

Gatevalve

rota

met

e rExpansion

Contraction

ReductionEnlargement

PI PI

T0 PT T0 PT

流體流動實驗裝置圖

Trap

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Fundamentals

Pipes are connected by: screws, welding, flanges; materials: many choices such as steel, PP, PVC, glass, ceramics etc; Pipe specs: size, wall thickness; nominal value for diameter may have different meaning for different pipes (outside, inside, none above); often follow some standards such as IPS, NPS; Selection of pipe size: mainly due to cost: material, installation, flow rate, density characteristics; power required; (cost ~ dia^1.5; power ~ dia^-4.8) Fluids are powered by pumps;

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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

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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

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Function of surface roughness

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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

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Various Flowmeters

orifice meter, Venturi meter, rotameter, etc. discharge coefficient = f(Re); for orifice meter: Vo = Co √(2 gc P/) Co determined experimentally

圖 A2-2 銳孔流量計之流出係數與 Re 關係。 其測壓點屬 corner tapCo can be assume to be 0.61 for large Re

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Venturi flowmeter and its discharge coefficient

Vo= Cv/√(1-4) √(2 g (ΔP/) = (d/D)For well designed meter, Cv usually about 0.98More expensive, more space;

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Pictures from Google to show different design of rotameter

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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

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Ultrasonic Flow Meter

non-invasive; (intrusive) two types: Doppler type (frequency shift ~ velocity) and transit time type (t ~ velocity) taken from Flow meter directory

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Universal flow monitors (UFM) webpage

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Consideration: Durability, pressure loss, control ability etc.

Check valve: one direction flow

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Pump performance: (taken from Walrus webpage)

Positive displacement pump

Centrifugal pump