Week 1Unit ConversionsConservation of MassIdeal GasNewtonian Fluids, Reynolds No.

Week 2Pressure Loss in Pipe FlowPressure Loss ExamplesFlow Measurement and ValvesPump Calcs and Sizing

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 = 2LD

C f ρv 2

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.

Head vs. ΔP

Head/Pressure loss in Fittings and Valves Reference Sheet

gPhead

Δ

Consider the previous example. How would the pressure drop change if the pipework included twelve 90 elbows and one fully open globe valve?

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

€

˙ 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

€

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