Week 1 – Engineering Agenda Introductions Why should I care about engineering? Motivation Dimensions and Unit Conversion Examples Ideal Gas Law Conservation.

Week 1 – Engineering Agenda

• Introductions• Why should I care about engineering?• Motivation• Dimensions and Unit Conversion

• Examples• Ideal Gas Law• Conservation of Mass

• Examples• Newtonian Fluids and Viscosity• Laminar and Turbulent Flow• Friction/Pressure Loss in Pipe Flow

Why is engineering important in brewing?1. 2.3.

What Engineering Decisions/Designs are Needed in the Brewing Process?

Some Steps in the Brewing Process• Malting• Mashing In• Mashing• Lautering• Wort Clarification and Cooling• Fermentation• Carbonization• Pasteurization• Packaging

Our Approach – Learn the fundamentals, then apply them to brewing

First 8 Weeks – Slightly more fundamentalsSecond 6 Weeks – Slightly more application

Also, plenty of practice for the exam!

A Typical DayMorning – Lecture new material, work

example problems, discussionsAfternoon – Practice, practice, get a

beer, practice some more!

General Problem Solving Methodology1. Identify the “Type” of Problem2. Principles and Equations3. Simplify and Identify Properties

Needed4. Get Properties (Tables, Equations,

etc.)5. Solve for Unknown, Calculations6. Interpret Results

a) Are the Results Reasonable?b) What Do they Mean?

Dimension – Quantifiable physical entity• Primary - Name them…• Secondary - Calculated from primary

Unit – Metric used to measure dimension• Base – m, kg, s, K, A, mole• Derived – From base units (J, N, W)

Dimensions or Units? “The temperature is 37 outside.” “Increase the psi’s.” “This light bulb will save you 2 kW per day.”

Unit Conversion – Just Multiply by 1.0

Units Example 1What is the power consumed by a 100 Watt light bulb, in horsepower(1 horsepower = 0.746 kW)?

Units Example 2A pressure gauge indicates that the absolute pressure inside of a vessel

is 350 psig (or psi gauge). The vessel is rated to 50 bar. Should we run for

cover?

Units Example 3A cylindrical tank has a 10 foot

diameter and 15 foot height. What volume of fluid will the tank hold in gallons and in hectoliters.

The Ideal Gas Equation

PV = mRTPV = NRuT

R = Ru / M

For a closed system (no mass in or out)

€

P1V1

T1

=P2V2

T2

Ideal Gas ExampleA 2 m3 tank is filled to an absolute pressure of 50 bar using an air compressor. After the tank has been filled, it’s temperature is 75C. After 24 hours, the tank cools to 15C.

a) Determine the mass of air in the tank.b) Determine the pressure in the tank after it has cooled.

Conservation of MassMass entering system

- Mass leaving systemMass accumulation in system

€

min − mout = Δmsystem

€

min

€

mout

€

Δmsystem

€

˙ m =m

t

€

m = ˙ m t

Conservation of Mass Example 1500 gallons of beer is initially held in a tank. Beer flows into the tank at a rate of 2.0 gallons per minute (gpm) an it flows out of the tank at 5.0 gallons per minute. Determine:a. The volume of beer after 45 minutesb. The rate of change of the beer volumec. The time elapsed when the tank is empty d. The total amount of beer that left the tank

€

˙ m = ρvA

Can write separate conservation equations for different components of a mixture

Conservation of Mass Example 2Beer with 19% alcohol by weight is

mixed with water to create beer with 4.5% alcohol by weight. If the flow rate of 19% alcohol beer is 40 kg/min, what are the flow rates of 4.5% alcohol beer and water, in kg/min and gal/sec? Assume that the density of the beer is 1000 kg/m3

Fluid StaticsΔP = ρgh Pressure vs. Head

Fluid Statics Example 1Determine the gauge pressure at the

bottom of a 5 m deep tank of liquid water when the top is vented to the atmosphere.

Fluid Statics Example 2Determine the pressure at the bottom of a 5 m deep tank of air when the top is vented to the atmosphere.

Newtonian Fluids and ViscositySolid

Elastic – Returns to original shapePlastic – Partially returns to original

Fluid

Linear velocity profile while force

is applied

Force

Forcey

Surface Fixed

v

How are Fluids Characterized

A substance that continually deforms under an applied shear stress, no matter how small

Density – Mass per unit volumeSpecific Gravity – Fluid density / water densitySpecific Weight – Fluid weight per unit volume

ViscosityCommon language – “Thickness”Science/Eng language – “Ability of fluid to resist a force”

Newtonian Fluids and Viscosity

Shear - one fluid element sliding faster than another, like deck of cards

Newton’s Law for viscosity

Shear stress = dynamic viscosity x shear rate

Example – Boat airboat moving through water, air, honey

€

σ =F

A= μ

Δv

Δy

Forcey

v

Newtonian Fluids and Viscosity

Dynamic viscosity (order of magnitude, STP) Air 0.00001 Pa.sWater 0.001 Pa.sOlive Oil 0.1 Pa.sHoney 10 Pa.s

density

viscositydynamic viscositykinematic

Handling Newtonian Fluids

Conservation of Mass (Continuity)

in out

€

˙ m in = ˙ m out

€

˙ m = ρvA

€

˙ m = ˙ V ρ

€

˙ V = vA

Handling Newtonian Fluids – Example 1

Water (density = 1000 kg/m3) enters a 2.0” diameter pipe at 10 m/s. The pipe then expands to a 6.0” diameter.

a. Determine the water velocity at the outlet of the pipe.

b. Determine the mass flow rate.

c. Determine the volumetric flow rate.

Handling Newtonian Fluids – Example 2

At a hop drying facility, air enters a heater through a 1 m2 duct at 10 m/s, 10oC and atmospheric pressure (101 kPa). The air is heated to 60oC at constant pressure before leaving the heater. To ensure that the hops are not damaged during drying, the air must be slowed to 5 m/s before entering the drying bed. R for air = 0.287 kJ/kg.K. Determine:

a. The inlet mass and volume flowrates of air

b. The cross sectional area of the drying bed

Reynolds NumberLaminar flow - “low” flow rates, viscous forces most significantTurbulent flow - “high” flow rates, inertial

forces most significant

Re < 2300 Laminar2300 < Re < 5000 TransitionalRe > 5000 Fully Turbulent

D

mD

4

Re

Reynolds NumberExample

Recall the previous example:

Water enters a 2.0” diameter pipe at 10 m/s and it exits through a 6” pipe.

Determine if the flow is laminar, transitional or turbulent in the 2.0” and 6.0” pipes. The dynamic viscosity of the water is 0.001 Pa.s.

Entrance Region and Fully Developed Flow

Laminar Flow:

Turbulent Flow:

Le

Re06.0 D

Le

6

1

Re4.4 D

Le

Entrance Region and Fully Developed FlowExample

Recall the previous example:

Water enters a 2.0” diameter pipe at 10 m/s and it exits through a 6” pipe.

Determine the entrance length of the inlet (2.0” diameter) pipe.

Fully Developed Velocity Profiles

Integrating to get the volumetric flow rate and average velocity, we get…

Laminar Flow:

Turbulent Flow:

Determine the maximum velocities of fully developed flow through the 2.0” and 6.0” pipes in our ongoing example.

50.0max

u

u

82.0max

u

u

Friction Losses in Pipes

found on Moody Chart handout

Determine the pressure drops over 20 meters of pipe for the 2.0” and 6.0” pipes in our ongoing example (in in H2O, psi, and kPa).€

C f

€

ΔP = 2L

DC f ρv 2

Reading

IntroductionSingh – 1.1, 2, 5, 6, 8, 9, 11, 14, 17, 22

Fluid FlowFrom Week 1, Singh – 2.2, 3, 4, 5Week 2, Singh – 2.1, 6, 7, 9