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Week 1Unit ConversionsConservation of MassIdeal GasNewtonian Fluids, Reynolds No.Pressure Loss in Pipe Flow
Week 2Pressure Loss ExamplesFlow Measurement and ValvesPump Calcs and Sizing
1000 gallons of wort is transferred to a kettle through a 15 m long, 4 cm diameter pipe with a roughness of 0.01 mm. The wort flows at a velocity of 1.2 m/s and assume that its physical properties are the same as those of water.
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, assuming that the wort remains at 72C.
d) Would P change if the wort were at 20C?
Head vs. P
Head/Pressure loss in Fittings and Valves Reference Sheet
g
Phead
Consider the previous example. How would the pressure drop change if the pipework includes twelve 90 elbows and one fully open globe valve?
Valves – Brewery Applications
Product Routing – Tight shutoff, material compatibility, CIP critical
Butterfly and mixproof
Service Routing – Tight shutoff and high temperature and pressure
Butterfly, Ball, Gate, Globe
Flow Control – Precise control of passage areaGlobe (and needle), Butterfly
Pressure Relief – Control a downstream pressure
Valves – Globe Valve
Single 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 control
Can be automated
Valves – Mix-proof Double Seat
Two separate sealing elements keeping the two fluids separated.
Keeps fluids from mixing
Immediate indication of failure
Automated, Sanitary apps
Easier 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
Bernoulli Equation
Notice how this works for static fluids.
€
P +1
2ρv 2 + ρgz = Constant
Flow Measurement – Oriface Meter
Cd accounts for frictional loss, 0.65
Simple design, fabrication
High turbulence, significant uncertainty
2
1
2
2
1
2
AA
PACQ d
P1 P2
Flow Meas. – Venturi Meter
Less frictional losses, Cd 0.95
Low pressure drop, but expensive
Higher accuracy than orifice plate
2
1
2
2
1
2
AA
PACQ d
P1P2
Flow Meas. – Variable Area/Rotameter
Inexpensive, good flow rate indicator
Good for liquids or gases
No remote sensing, limited accuracy
WeightDragForces
mgvCdrag 2
2
10
vAV
Flow Measurement - Pitot Tube
Direct velocity measurement (not flow rate)
Measure P with gauge, transducer, or manometer
P1
P2
1 2
2
2
21v
PP
v
Flow Measurement – Weir
Open channel flow, height determines flow
Inexpensive, good flow rate indicator
Good for estimating flow to sewer
Can measure height using ultrasonic meter
Flow Measurement – Thermal Mass
Measure gas or liquid temperature upstream and downstream of heater
Must know specific heat of fluid
Know power going to heater
Calculate flow rate
Pumps
z = static headhf = head loss due to friction
Pump
fss
ss hρg
Pzh HeadSuction
Suction Delivery
fdd
dd hρg
Pzh HeadDelivery
fsfdsd
sdsd hhρg
PPzzhh Head Total
PumpsDistanceForceWork
DistanceAreaArea
ForceWork
time
DistanceArea
Area
Force
time
WorkPower
Flowrate VolumeΔPPower
ghVPV Output Power
Efficiency Pump
OutputPower InputPower
Pumps
Calculate 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.
If the electrical efficiency is 95%, calculate the electrical power required.
Denisity of Water = 1000 kg/m3
1 bar = 100 kPa
Pumps
A 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. 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 NPSH
Avoid Cavitation
z = static headhf = head loss due to friction
fs
v hP
ρg
Pz NPSH Available ps
s
Pumps
A 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 Sizing
1. Volume Flow Rate (m3/hr or gpm)
2. Total Head, h (m or ft)
2a. P (bar, kPa, psi)
3. Power Output (kW or hp)
4. NPSH Required
hgP
PumpsCentrifugal
Impeller spinning inside fluid
Kinetic energy to pressure
Flow controlled by Pdelivery
Positive Displacement
Flow independent of Pdelivery
Many configurations
Centrifugal Pumps
Constantρgzρv2
1P 2
Impeller
SuctionVolute Casting
Delivery
Centrifugal Pumps
Flow accelerated (forced by impeller)
Then, flow decelerated (pressure increases)
Low pressure at center “draws” in fluid
Pump should be full of liquid at all times
Flow controlled by delivery side valve
May operate against closed valve
Seal 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-Q Chart
Head
(or P)
Volume Flow Rate
Increasing Impeller Diameter
A B C
Centrifugal PumpsH-Q Chart
Head
(or P)
Volume Flow Rate
A B C
Increasing Efficiency
Required NPSH
Centrifugal PumpsH-Q Chart
Head
(or P)
Volume Flow Rate
A B C
Centrifugal PumpsH-Q Chart
Head
(or P)
Volume Flow Rate
Required Flow
CapacityActual Flow
Capacity
Required Power
Pump Sizing Example
Requirements8 gpm100 feet of head
Choose the proper impellerDetermine the power consumed by the pumpDetermine the NPSH required