so far: conservation of mass, flow rates fluid flow, re no., laminar/turbulent
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So Far:Conservation of Mass, Flow Rates
Fluid Flow, Re No., Laminar/TurbulentPressure Drop in PipesBernoulli’s EquationFlow Measurement, ValvesTotal Head, Pump Power, NPSH
This Week:Pump Sizing, Types of PumpsConservation of Energy
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
Pumps
Centrifugal
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
Centrifugal PumpsPump sizing example.
Let’s say we need a pump for the following application:
Total head: 40 mFlow rate: 2.5 m3/hrNPSH available: 2 m
Using the pump curve provided last week. Select the appropriate impeller and determine the flow capacity with that impeller, pump power input, NPSH required and efficiency.
Centrifugal Pumps
What if available NPSH is less than required NPSH?
Increase Available NPSH1. Increase suction static head (pump location)
2. Increase suction side pressure
3. Decrease fluid vapor pressure
4. Reduce friction losses on suction side
Decrease Required NPSH1. Reduce pump speed
2. Select a different pump
Centrifugal Pumps
Curves created for specific speed, viscosity and density
Often, use more charts or correction factors to “fine tune” pump selection
Variable speed motor has same effect as impeller size
Multiple pump/impeller combinations may work
Centrifugal Pumps
Closed ImpellerMost common, low solidsWater, beer, wortFlash pasteurizationRefrigerants
Open ImpellerLower pressuresSolids okayMash to lauter turnLiquid yeast, wort, hops
Positive Displacement Pumps
Theory: Volume dispensed independent of delivery head
Practice: As delivery head increases, some slippage or leakage occurs
Speed used to control flow rate, use of valves could cause serious damage
Self-priming
Good for high viscosities, avoiding cavitation
Positive Displacement Pumps
Piston Pump
Volumetric Efficiency High Pressures
Metering hop compounds, detergents, sterilents
Suction Valve
Delivery Valve
Positive Displacement Pumps
Peristaltic Pump
Positive Displacement Pumps
Gear Pump
High Pressures
No Pulsation
High Viscosity Fluids
No Solids
Difficult to Clean
Positive Displacement Pumps
Lobe Rotor Pump
Both lobes driven
Can be sterilized
TransferYeastTrubBulk Sugar Syrup
Liquid-Solid Separation
Types of FiltrationGravity, Vacuum, Pressure, Centrifugal
Driving Force
MechanicalDialysis Electrostatic Magnetic
Filtration Sedimentation
FiltrationMedia
Glass fiberPaper fabricMonofilament clothMetal or plastic mesh or screenPack beds
Bridging effect of filter cloth
Filter cake buildup becomes
“filter media”
Filtration
Performance of Filters• Ability to retain solids (high surface area)• Low flow resistance• Mechanical strength• Low cost• Inert to cleaning/processing chemicals
Brewery applications of filtrationMash or Lauter tun – gravity filtrationFiltering wort and beer – pressure filtrationSeparating beer from yeast – pressure filter
Liquid-Solid Separation
Sedimentation – gravity or centrifugal
Terminal settling velocity – time required
TSV increases with:
Larger particles
Greater density difference
between fluid, particle
Lower fluid viscosity
Next Slide: Shift Gears to Properties, First Law
Weight
Drag Force
Steam Table ExamplesDetermine the phase, enthalpy and specific volume of the following:
P = 1 bar, T = 25C
P = 1 bar, T = 160C
T = 150C, v = 0.5 m3/kg
ExampleDetermine the amount of energy required to heat 500 gallons of water from 20C to 220C at constant pressure (1.0 bar).
Enthalpy of fusion: 333.55 kJ/kgEnthalpy of vaporization: 2260 kJ/kgSpecific heat of ice: 2.1 kJ/kg.KSpecific heat of liquid water: 4.2 kJ/kg.KSpecific heat of steam (cp): 2.2 kJ/kg.K)
1 m3 = 264.2 gal
Laws of Thermodynamics• First Law – Energy is conserved• Second Law – Energy has quality, processes go in certain directions only
Forms of Energy• Potential energy = mgh• Kinetic energy = (0.5)mv2
• Internal energy (U) – microscopic forms
Conservation of Energy
systemoutin dt
dEEE
Systemoutin EEE
Energy Interactions• Heat transfer – Temperature difference• Work – Shaft, electrical, boundary, etc.• Mass flow – U + PV = Enthalpy (H)
Closed System Energy Equation
systemoutout
outoutoutout
inin
inininin
Egzv
umWQ
gzv
umWQ
2
2
2
2
1212 )( TTmcuumE vsystem No Phase Change
Open System Energy Equation
for steady flow systems
or
dt
dEgz
vhmWQ
gzv
hmWQ
systemout
outoutoutoutout
inin
inininin
2
2
2
2
0dt
dEsystem
tQQ t
ExampleA 2 m3 tank is filled to a pressure of 150 psig using an air compressor. After the tank has been filled, it’s temperature is 157F. Over the course of 20 hours, the tank cools to 56F. (cv = 0.718, cp = 1.04 kJ/kg.K).
a) Determine the mass of air in the tank.b) Determine the pressure in the tank after it has cooled.c) Determine the amount and average rate of heat transfer during the cooling process in kJ and W, respectively.
A 500 gallon water tank is filled with 220 gallons of hot water at 80C and 280 gallons of cold water at 10C. Assume that the specific heat of water is 4.2 kJ/kg.K.
a) Determine the temperature in the tank after it has been filled.
b) How much heat must be added to the tank to bring its temperature to 65C?
c) If a 30 kW electric heater is used, how long will the heating process take?
500 kg of grain (25C) is mixed with hot (80C) and cold (10C) water for mashing. The water to grain ratio (by weight) is 3:1 and the specific heat capacities of the water and grain are 4.2 and 1.7 kJ/kg.K, respectively.
a) If the desired “mash in” temperature is 38C, how much hot and cold water should be added?
(Continued) A three step mashing process, with 20 minute-long rests at 50, 62 and 72C, is desired. The mash should be heated quickly, but not too quickly between rests; with an optimal rate of 1C per minute. Neglect heat losses to the surroundings.
b) Plot the mash temperature vs. time.
c) Determine the heating power required, in kW.
d) Determine the total heat required for the mashing process, in kJ.
Two types of heat sources are available for mashing, electric resistance heaters and steam. The steam enters a heating jacket around the mash as dry, saturated steam at 300 kPa and it exits the system as wet, saturated steam at the same pressure (enthalpy of vaporization = 2150 kJ/kg).
(e) What is the total power required for the electric heaters, in kW?
(f) If steam is used, what is the total mass of steam required, in kg?
At the location of our brewery, electricity costs $0.14/kW-hr and the steam can be generated for $0.03 per kg.
(g) What is the mashing cost when electric resistance heaters are used?
(h) What is the cost with steam?
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