1. Week 1 – Engineering Agenda
Introduction
Terminology
Dimensions and Unit Conversion
Ideal Gas Law
Conservation of Mass
Newtonian Fluids and Viscosity
Laminar and Turbulent Flow
Friction/Pressure Loss in Pipe Flow

2. Why is engineering important in brewing?1. 2. 3.
What engineering decisions/designs are needed in the brewing process?

3. Our Approach – Learn the fundamentals, then apply them to brewing
A Typical Week
Thurs - Recap Last Week’s Material
Thurs - Lecture new material
Thurs - Example calculations
Fri - More examples
Work together – Benefits everyone!
Create neat, organized solutions
Stick with it

4. General Problem Solving Methodology
Identify the “Type” of Problem
Principles and Equations
Simplify and Identify Properties Needed
Get Properties (Tables, Equations, etc.)
Solve for Unknown, Calculations
Interpret Results
Are the Results Reasonable?
What Do they Mean?

5. 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.”

6. Unit Conversion – Just Multiply by 1.0
Units Example 1
What is the power consumed by a 100 Watt light bulb, in horsepower
(1 horsepower = kW)?

7. Units Example 2
A 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 3
A cylindrical tank has a 3 m diameter and 5 m height. What volume of fluid will the tank hold in gallons and in hectoliters.

8. The Ideal Gas Equation
PV = mRT
PV = NRuT
R = Ru / M
For a closed system (no mass in or out)

9. Ideal Gas Example
A 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 75C. After 24 hours, the tank cools to 15C.
a) Determine the mass of air in the tank.
b) Determine the pressure in the tank after it has cooled.

10. Conservation of Mass
Mass entering system
- Mass leaving system
Mass accumulation in system

11. Conservation of Mass Example 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:
The volume of beer after 45 minutes
The rate of change of the beer volume
The time elapsed when the tank is empty
The total amount of beer that left the tank

12. Can write separate conservation equations for different components of a mixture
Conservation of Mass Example 2
Beer 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 kg/m3

13. Fluid Statics
ΔP = ρgh Pressure vs. Head
Fluid Statics Example 1
Determine 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 2
Determine the pressure at the bottom of a 5 m deep tank of air when the top is vented to the atmosphere.

14. Newtonian Fluids and Viscosity Solid
Elastic – Returns to original shape
Plastic – Partially returns to original
Fluid
Linear velocity profile while force is applied
Force
Surface Fixed
Force y v

15. How are Fluids Characterized
A substance that continually deforms under an applied shear stress, no matter how small
Density – Mass per unit volume
Specific Gravity – Fluid density / water density
Specific Weight – Fluid weight per unit volume
Viscosity
Common language – “Thickness”
Science/Eng language – “Ability of fluid to resist a force”

16. 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
Force y v

17. Newtonian Fluids and Viscosity
Dynamic viscosity (order of magnitude, STP)
Air Pa.s
Water Pa.s
Olive Oil Pa.s
Honey Pa.s

18. Handling Newtonian Fluids Conservation of Mass (Continuity)
out

19. Handling Newtonian Fluids – Example 1
Water (density = 1000 kg/m3) enters a 5 cm diameter pipe at 10 m/s. The pipe then expands to a 10 cm diameter.
a. Determine the water velocity at the outlet of the pipe.
b. Determine the mass flow rate.
c. Determine the volumetric flow rate.

20. 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 = kJ/kg.K. Determine:
The inlet mass and volume flowrates of air
The cross sectional area of the drying bed

21. Reynolds Number
Laminar flow - “low” flow rates, viscous forces most significant
Turbulent flow - “high” flow rates, inertial forces most significant
Re < Laminar
2300 < Re < 5000 Transitional
Re > Fully Turbulent

22. Reynolds Number
Example
Recall the previous example:
Water enters a 5 cm diameter pipe at 10 m/s and it exits through a 10 cm pipe.
Determine if the flow is laminar, transitional or turbulent in the 5 cm and 10 cm pipes. The viscosity of the water is Pa.s.

23. 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 5 cm and 10 cm pipes in our ongoing example.

24. found on Moody Chart handout
Friction Losses in Pipes
found on Moody Chart handout
Determine the pressure drops over 80 meters of pipe for the 5 cm and 10 cm pipes in our ongoing example.