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.

€

C f

€

ΔP = 2L

DC f ρv 2

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

Valves – Brewery Applications

Product Routing – Tight shutoff, material compatibility, CIP critical

Butterfly and mixproof

Service Routing – Tight shutoff and high temperature and pressure

Ball, Gate, Globe

Flow Control – Precise control of passage areaGlobe (and needle), Butterfly

Pressure Relief – Control a downstream pressure

Flow Measurement Principle:

Bernoulli Equation

Notice how this works for static fluids.

€

P +1

2ρv 2 + ρgz = Constant

Flow Measurement – Orifice Meter

Cd accounts for frictional loss, 0.65

Simple design, fabrication

High turbulence, significant uncertainty€

˙ V = Cd A2

2ΔP

ρ

1− A2A1

⎛ ⎝ ⎜ ⎞

⎠ ⎟2

P1 P2

Flow Meas. – Venturi Meter

Less frictional losses, Cd 0.95

Low pressure drop, but expensive

Higher accuracy than orifice plate€

˙ V = Cd A2

2ΔP

ρ

1 − A2A1

⎛ ⎝ ⎜ ⎞

⎠ ⎟2

P1P2

Flow Meas. – Variable Area/Rotameter

Inexpensive, good flow rate indicator

Good for liquids or gases

No remote sensing, limited accuracy

WeightDragForces

€

0 = Cdrag12 ρAv 2 − mg

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

Flow Measurement – Magnetic

Faradays Law

Magnetic field applied to the tube

Voltage created proportional to velocity

Requires a conducting fluid (non-DI water)

Flow Measurement – Magnetic

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 ΔΔ 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.

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. 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 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 ΔΔ

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-V 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

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