Transcript Unit Operation Lab - National Tsing Hua University

Unit Operation Lab
K S Chou
Ch E, N T H U
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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;
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 Fermentation reactor: one example of solidliquid-gas system
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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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For sudden or gradual change in diameter:
(expansion/ contraction): vortex formation cause
energy loss
 One special example: hf = Ke Va2/2gc, with Ke = (1Aa/Ab)2; e: expansion
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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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PT ( 壓力計)
90º elbow
PT (壓力計接頭)
Straight pipe
180º elbow
water
Trap
Storage
tank
T0 PT
T0 PT
PI
PI
Buffer
tank
rotameter
Orifice meter
PI
pump
Globe valve
45º elbow
flange
Reduction
Enlargement
Ball
valve
Venturi meter
Expansion
Gate
valve
Contraction
流體流動實驗裝置圖
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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
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Venturi flowmeter and
its discharge coefficient
Vo= Cv/√(1-4) √(2 g
(ΔP/)
 = (d/D)
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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; two types: Doppler type
(frequency shift ~ velocity) and transit time type
(t ~ velocity)
 taken from Flow meter directory
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