Week 1 – Engineering Agenda• Introductions and Photos• Why should I care about engineering?• Motivation for the DB Exam• 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.

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

Learn the Fundamentals, Apply to Brewing

“Margaret’s Story…”

For the candy… who are these people?

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 low flow toilet will save you 2 gpm (gallons per minute) 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 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 hectaliters.

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 a 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

Conservation of MassRate of mass entering system

- Rate of mass leaving systemRate of mass accumulation in system

€

˙ m in − ˙ m out = dmdt system

inm

outmsystemdt

dm

€

˙ m = mt

€

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

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˙ m = ρvA

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?

Fluid StaticsΔP = ρgh (Also use to convert

between pressure and pressure ‘head.’)

Fluid Statics Example 1Determine the 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

Newtonian Fluids and Viscosity

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

Newton’s Law for viscosity

Shear stress = viscosity x shear rate

Many units for viscosity – Pa s, poise or cenitpoise are common

dydv

Forcey

v

Newtonian Fluids and ViscosityDynamic 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

Newtonian Fluids and ViscosityExample

Determine the dynamic () and kinematic () viscosities of water and air at 300 and 500 K.

Handling Newtonian FluidsConservation of Mass (Continuity)

in out

outin mm

outoutoutininin AvρAvρ

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˙ m = ˙ V ρ

Handling Newtonian FluidsExample

Steam enters a 2.0” diameter pipe at 10 m/s, 1 bar and 150C. The pipe expands to a 6.0” diameter and the water exits the system at 20C.

a. Determine the water velocity at the outlet of the pipe. b. Determine the mass flow rate.c. Determine the volumetric flow rate at the inlet and exit of the system.

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

DmD

4Re

Reynolds NumberExample

Recall the previous example:

Steam enters a 2.0” diameter pipe at 10 m/s, 1 bar and 150C. The pipe

expands to a 6.0” diameter and the water exits the system at 20C.

Determine if the flow is laminar, transitional or turbulent in the 2.0” and 6.0” pipes.

Entrance Region and Fully Developed Flow

Laminar Flow:

Turbulent Flow:

Le

Re06.0 DLe

61

Re4.4 DLe

Entrance Region and Fully Developed FlowExample

Recall the previous example:

Steam enters a 2.0” diameter pipe at 10 m/s and 150C. The pipe expands to a 6.0” diameter and the water exits the system at 20C.

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

Determine the entrance length if air instead of water.

Fully Developed Velocity ProfilesIntegrating 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, HT p. 191

Determine the pressure drops over 25 feet of pipe for the 2.0” and 6.0” pipes in our ongoing example (in in H2O, psi, and kPa).

22 uLDPf

Δ

f