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

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

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

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?

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

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.

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

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.

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

Conservation of Mass Example 1 500 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

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 1000 kg/m3

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.

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

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”

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

Newtonian Fluids and Viscosity Dynamic viscosity (order of magnitude, STP) Air 0.00001 Pa.s Water 0.001 Pa.s Olive Oil 0.1 Pa.s Honey 10 Pa.s

Handling Newtonian Fluids Conservation of Mass (Continuity) out

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.

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: The inlet mass and volume flowrates of air The cross sectional area of the drying bed

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

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 0.001 Pa.s.

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.

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.