week 1 unit conversions mass and volume flow ideal gas newtonian fluids, reynolds no . week 2
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Week 1 Unit Conversions Mass and Volume Flow Ideal Gas Newtonian Fluids, Reynolds No . Week 2 Pressure Loss in Pipe Flow Pressure Loss Examples Flow Measurement and Valves Pump Calcs and Sizing. - PowerPoint PPT PresentationTRANSCRIPT
Week 1Unit ConversionsMass and Volume FlowIdeal GasNewtonian Fluids, Reynolds No.
Week 2Pressure Loss in Pipe FlowPressure Loss ExamplesFlow Measurement and ValvesPump Calcs and Sizing
1000 gallons of wort is transferred from a kettle through a 100 m long, 4 cm diameter pipe with a roughness of 0.01 mm. The wort flows at an average velocity of 1.2 m/s and assume that its physical properties are the same as those of water (μ = 0.001 Pa.s).
a) Determine the time required to transfer all of the wort to the boil kettle, in min.
b) Determine the Reynolds Number.c) Determine the pressure drop in the pipe.
Friction Losses in Pipes
found on Moody Chart handout
Determine the pressure drop of water, moving through a 5 cm diameter, 100 m long pipe at an average velocity of 5 m/s. The density of the water is 1000 kg/m3 and the viscosity is 0.001 Pa.s. The pipe roughness is 0.05 mm.
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C f
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ΔP = 2LD
C f ρv 2
Valves – Globe ValveSingle Seat
- Good general purpose- Good seal at shutoff
Double Seat- Higher flow rates- Poor shutoff (2 ports)
Three-way- Mixing or diverting- As disc adjusted, flow to one channel increased, flow to other decreased
Valves – Butterfly Valve
Low Cost“Food Grade”Poor flow controlCan be automated
Valves – Mix-proof Double SeatTwo separate sealing elements
keeping the two fluids separated.
Keeps fluids from mixingImmediate indication of failureAutomated, Sanitary appsEasier and Cheaper than
using many separate valves
Valves – Gate Valve
Little flow control, simple, reliable
Valves – Ball Valve
Very little pressure loss, little flow control
Valves – Brewery ApplicationsProduct Routing – Tight shutoff, material
compatibility, CIP criticalButterfly and mixproof
Service Routing – Tight shutoff and high temperature and pressure
Ball, Gate, GlobeFlow Control – Precise control of passage area
Globe (and needle), ButterflyPressure Relief – Control a downstream
pressure
Flow Measurement Principle:Bernoulli Equation
Notice how this works for static fluids.
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P + 12
ρv 2 + ρgz = Constant
Flow Measurement – Orifice Meter
Cd accounts for frictional loss, 0.65Simple design, fabricationHigh turbulence, significant uncertainty
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˙ V = Cd A2
2ΔPρ
1 − A2A1
⎛ ⎝ ⎜ ⎞
⎠ ⎟2
P1 P2
Flow Meas. – Venturi Meter
Less frictional losses, Cd 0.95Low pressure drop, but expensiveHigher accuracy than orifice plate€
˙ V = Cd A2
2ΔPρ
1 − A2A1
⎛ ⎝ ⎜ ⎞
⎠ ⎟2
P1P2
Flow Meas. – Variable Area/Rotameter
Inexpensive, good flow rate indicatorGood for liquids or gasesNo remote sensing, limited accuracy
WeightDragForces
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0 = Cdrag12 ρAv 2 − mg
vAV
Flow Measurement - Pitot Tube
Direct velocity measurement (not flow rate)Measure ΔP with gauge, transducer, or
manometer
P1
P2
1 2
2
2
21vPP
v
Flow Measurement – Weir
Open channel flow, height determines flowInexpensive, good flow rate indicatorGood for estimating flow to sewerCan measure height using ultrasonic meter
Flow Measurement – Thermal Mass
Measure gas or liquid temperature upstream and downstream of heater
Must know specific heat of fluidKnow power going to heaterCalculate flow rate
Flow Measurement – Magnetic
Faradays LawMagnetic field applied to the tubeVoltage created proportional to velocityRequires a conducting fluid (non-DI water)
Flow Measurement – Magnetic
Pumps
z = static headhf = head loss due to friction
Pump
fss
ss hρgP
zh HeadSuction
Suction Delivery
fdd
dd hρgP
zh HeadDelivery
fsfdsd
sdsd hhρg
PPzzhh Head Total
PumpsDistanceForceWork
DistanceAreaAreaForceWork
timeDistanceArea
AreaForce
timeWorkPower
Flowrate VolumeΔPPower
ghVPV ΔΔ Output Power
Efficiency PumpOutputPower InputPower
PumpsCalculate the theoretical pump power
required to raise 1000 m3 per day of water from 1 bar to 16 bar pressure.
If the pump efficiency is 55%, calculate the shaft power required.
Denisity of Water = 1000 kg/m3
1 bar = 100 kPa
PumpsA pump, located at the outlet of tank A,must transfer 10 m3 of fluid into tank B in 20 minutes or less. The water level in tank A is 3 m above the pump, the piperoughness is 0.05 mm, and the pumpefficiency is 55%. The fluid density is 975 kg/m3 and the viscosity is 0.00045Pa.s. Both tanks are at atmosphericpressure. Determine the total head andpump input and output power.
Tank A
Tank B
8 m
15 m
4 m
Pipe Diameter, 50
mm
Fittings = 5 m
Pumps
Need Available NPSH > Pump Required NPSHAvoid Cavitationz = static headhf = head loss due to friction
fs
v hP
ρg
Pz NPSH Available ps
s
PumpsA pump, located at the outlet of tank A,must transfer 10 m3 of fluid into tank B in 20 minutes or less. The water level in tank A is 3 m above the pump, the piperoughness is 0.05 mm, and the pumpefficiency is 55%. The fluid density is 975 kg/m3 and the viscosity is 0.00045Pa.s. The vapor pressure is 50 kPa andthe tank is at atmospheric pressure.Determine the available NPSH.
Tank A
Tank B
8 m
15 m
4 m
Pipe Diameter, 50
mm
Fittings = 5 m
Pump Sizing1. Volume Flow Rate (m3/hr or gpm) 2. Total Head, Δh (m or ft)
2a. ΔP (bar, kPa, psi)3. Power Output (kW or hp)4. NPSH Required
hgP ΔΔ
PumpsCentrifugal
Impeller spinning inside fluidKinetic energy to pressureFlow controlled by Pdelivery
Positive DisplacementFlow independent of Pdelivery
Many configurations
Centrifugal Pumps
Constantρgzρv21P 2
Impeller
SuctionVolute Casting
Delivery
Centrifugal PumpsFlow accelerated (forced by impeller)Then, flow decelerated (pressure increases)Low pressure at center “draws” in fluidPump should be full of liquid at all timesFlow controlled by delivery side valveMay operate against closed valveSeal between rotating shaft and casing
Centrifugal PumpsAdvantages
Simple construction, many materialsNo valves, can be cleaned in placeRelatively inexpensive, low maintenanceSteady delivery, versatileOperates at high speed (electric motor)Wide operating range (flow and head)
DisadvantagesMultiple stages needed for high pressuresPoor efficiency for high viscosity fluidsMust prime pump
Centrifugal PumpsH-V Chart
Head
(or ΔP)
Volume Flow Rate
Increasing Impeller Diameter
A B C
Centrifugal PumpsH-Q Chart
Head
(or ΔP)
Volume Flow Rate
A B C
Increasing Efficiency
Required NPSH
Centrifugal PumpsH-Q Chart
Head
(or ΔP)
Volume Flow Rate
A B C
Centrifugal PumpsH-Q Chart
Head
(or ΔP)
Volume Flow Rate
Required Flow
CapacityActual Flow
Capacity
Required Power
Pump Sizing Example
Requirements100 gpm45 feet of head
Choose the proper impellerDetermine the power input to the pump
Pressure Drop Example
Water flows through a 10 cm diameter, 300 m long pipe at a velocity of 2 m/s. The density is 1000 kg/m3, the viscosity is 0.001 Pa.s and the pipe roughness is 0.01 mm. Determine:
a. Volume flow rate, in m3/sb. Mass flow rate in kg/sc. Pressure loss through the pipe, in Pad. Head loss through the pipe meters