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 (natural gas), liquid (tap water),
solid, bubbled liquid, slurry, gas-solid (fluidization), solidliquid-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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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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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/)
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)
 Claim to account for 20% of all flowmeters
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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Electromagnetic Flowmeters
CEP, May 2010
 Advantages: no pressure drops; no moving parts
subject to wear; linear output over a wide range
of velocities;
 Disadvantage: fluid has to be conductive; often
have temperature limits; (mho = 1/ohm)
 One of the key technology: keeping magnetic
field constant ; electrode material will contact
process fluid and cleaning fluids (compatible
issue);
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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)
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