BAE 103 Energy in BiosystemsSpring 2012

Lecture 1 (Jan. 11): THINKING LIKE AN ENGINEER

The System Concept…….

Component 1 Input

Control

Rules

Control

Outputs Component 2

Control

Component 3Input

Input

Rules

Rules

Input

OU

TP

UT

S

Output

A very important concept…….

time

Amount Rate ProcessingComponent

Other examples of time rates….

time

Work Power

time

Volume Flow Fluid

time

Area Capacity Field

time

Distance Velocity

Basic Quantities, Properties, Parameters…….

Four basic Dimensions:Displacement (L)Mass (M)Time (T)Temperature (D)

Quantity Dimensions Units

Distance L meters (m), feet (ft)

Time T minutes, hours, seconds

Mass M kg, g, lbm

Temperature D oC, oF

Area L2 m2, ft2

Volume L3 m3, ft3

Velocity L/T m/s, km/hr, ft/s, mi/hr

Acceleration L/T2 m/s2, ft/s2

Mass density M/L3 kg/m3, g/cm3, lbm/ft3

Force ML/T2 N = kg-m/s2, lbf = lbm-ft/s2

Energy ML2/T2 J = N-m, cal, ft-lbf, BTU

Power ML2/T3 W = J/s, HP = 550 ft-lbf/s

Heat capacity L2/(T2-D) cal/(oC-g), BTU/(oF-lbm)

Table 1.1 Some fundamental parameters and dimensions

Fundamental Laws and Relationships

•Geometric equations•Area, Volumes, Perimeters• Physical Laws•Newton’s Laws of Motion• Conservation of Mass, Energy

Table 1.2 Some fundamental laws and equations which govern systems

Law or Equation Description Inputs/OutputF = m a∙ Newton’s 2nd law Force (F), mass (m),

acceleration (a), W = F d∙ Definition of work/energy Work/energy (W), Force (F),

distance (d) H = W/t Definition of power Power (H), Work/energy (W),

time (t)T = F r∙ Definition of torque Torque (T), Force (F),

radius (r) H = 2π T n∙ ∙ Definition of rotational power Power (H), radius (r),

Torque (T), rotational speed (n)

v = d/t Definition of velocity velocity (v), distance (d), time (t)

a = ∆v/t Definition of acceleration acceleration (a), change in velocity (∆v), time (t)

p = F/A Definition of pressure pressure (p), Force (F),area (A)

Q = v A∙ Definition of volume flow rate Volume flow rate (Q), velocity (v),

cross-section area (A)

Table 1.3 Geometric formulas

Shapes Formula

Rectangle:Area = Length X Width

A = l w∙

Perimeter = 2 X Length + 2 X WidthP = 2l + 2w

ParallelogramArea = Base X Height

A = b h∙

TriangleArea = 1/2 of the base X the height

A = 1/2 b h∙Perimeter = a + b + c

(add the length of the three sides)

Table 1.3 Geometric formulas

Trapezoid

Area, A = (b1 + b2)/2 h∙Perimeter, P = a + b1 + b2 + c

Circle

d = 2rc = pd = 2 pr

A = pr2

Rectangular SolidVolume = Length X Width X Height

V = l w h∙ ∙Surface = 2 l w + 2 l h + 2 w h∙ ∙ ∙ ∙ ∙ ∙

Table 1.3 Geometric formulas

PrismsVolume = Base X Height

v=b h ∙Surface = 2b + Ph (b is the area of the base P is the perimeter of the

base)

CylinderVolume = pr2 x height

V = pr2 hSurface = 2p radius x height

S = 2prh + 2pr2

PyramidV = 1/3 b h∙

b is the area of the baseSurface Area: Add the area of the base to the sum of the areas of all

of the triangular faces. The areas of the triangular faces will have different formulas for different shaped bases.

Table 1.3 Geometric formulas

ConesVolume = 1/3 pr2 x height

V= 1/3 pr2h Surface = pr2 + prs

S = pr2 + prs =pr2 + pr

SphereVolume = 4/3 pr3

V = 4/3 pr3

Surface = 4pr2

S = 4pr2

Table 1.4 Unit conversions

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Mass and Weight1 ounce = 437.5 grains = 28.35 grams1 pound = 16 ounces = 7,000 grains = 453.6 grams1 ton = 2,000 pounds1 kilogram = 1000 grams = 2.2046 pounds1 metric ton = 1000 kilograms

Length1 mile = 5,280 feet = 1,760 yards = 320 rods = 80 chains = 1.609 km1 chain = 66 feet = 22 yards = 4 rods = 100 links1 rod = 16.5 feet = 5.5 yards1 meter = 39.37 inch = 3.28 feet1 foot = 12 inches = 30.48 centimeters1 inch = 2.54 centimeters = 25.4 millimeters

Table 1.4 Unit conversions

Area1 hectare = 10,000 square meters = 2.47 acres1 acre = 160 square rods = 43,560 square feet = 0.405 hectares1 square mile = 640 acres

Volume1 cubic inch =16.39 cubic centimeters1 cubic foot = 1,728 cubic inches = 7.48 gallons1 cubic yard = 27 cubic feet1 gallon = 4 quarts = 8 pints = 231 cubic inches = 128 fluid ounces = 3.785

liters1 bushel = 1.244 cubic feet1 cubic meter = 1000 liters1 liter = 1000 cubic centimeters = 1000 milliliters

Time1 hour = 60 minutes = 3,600 seconds1 minute = 60 seconds

Table 1.4 Unit conversions

Water Volume/Mass Properties1 gallon = 8.34 pounds1 cubic inch = 0.03611 pounds1 cubic foot = 62.4 pounds 1 liter = 1 kilogram1 cubic centimeter = 1 gram1 cubic meter = 1,000 kilograms = 1 metric ton

Specific and Latent HeatSpecific Heat of Water – 1.0 Btu/pound/oF, 1.0 calorie/gram/oCSpecific Heat of Ice – 0.48 Btu/pound/oF, 0.48 calorie/gram/oCLatent Heat of Fusion for Ice – 144 Btu/pound, 80 calories/gramLatent Heat of Vaporization of Water – 970 Btu/pound, 540 calories/gram

Table 1.4 Unit conversions

Force, Work, Power and Energy1 calorie = 4.186 J1 Calorie = 1000 calories = 3.9683 Btu1 pound-force = 4.448 Newtons1 Newton = 1 kg-m/s2

1 Joule = 1 Newton-meter1 Btu = 1054 Joules = 252 calories = 780 feet-pounds-force1 kilowatt = 1000 Joules/second = 1 kilojoules/second1 kilowatt.hours = 3414 Btu 1 horsepower = 550 feet-pounds-force/second = 33,000 foot-pounds-force/minute1 horsepower = 0.746 kilowatts

Pressure 1 Pascal = 1 Newton/m2

1 atm = 101.325 kilo-Pascal = 14.7 pounds/square inch = 34.0 feet of H2O = 29.92 in Hg = 760 mm Hg

Example 1……

A runner covers a distance of 5.8 miles in 63 minutes. What is the runner’s average velocity (mi/hr)? If the runner can maintain this velocity for 2.5 hours, what distance will be travelled?

Example 2……

A tractor is mowing a 15.4 ha hay field. If the length of the cutter bar is 2.2 m and the average speed of the tractor is 10.3 km/hr, how long is required to mow the field (hr)?

Example 3……

A pump is filling a tank with dimensions: h = 15 ft, D = 25 ft. If 30 hours is required to fill the tank, what is the pumping rate (gal/min)? If the hose delivering water from the pump to the tank has an inside diameter of 4 in., what is the flow velocity of water in the hose (ft/sec)?

Example 4……

A tractor is pulling a wagon up a hill of 10% slope at a speed of 4 km/hr. If the load on the wagon has a mass of 5000 kg, what is the required power (kW)?

Importance and Power of Units and Dimensions…….

•Necessary to quantify systems parameters • Indicates “reasonableness” of calculations• Indicates validity of relationships between parameters• Can help determine relationships between parameters

BE Problem-Solving ProcedureGiven:1. Always draw a picture of the system.• Establishes relationships between

parameters.2. State all assumptions.3. Identify all factors/parameters and their units.

Required:4. Label unknown quantities with a question

mark.

BE Problem-Solving Procedure

Relationships:5. Write or derive the main equation which

contains the unknown required quantity.6. Algebraically manipulate the main equation to

solve for the required quantity.7. Write subordinate equations needed to

determine quantities in the main equation.• Indent subordinate equations.

BE Problem-Solving ProcedureSolution:8. Insert numerical quantities and their units into

equations.9. Ensure that units cancel correctly and check

for correct sign.10. Compute the answer.11. Mark the final answer, with its units, by

enclosing it in a box.12. Make sure the final anwer is physically

reasonable.13. Ensure that all questions have been answered.

Example 5…..

A combine grain harvester is operating in a field that yields 200 bu/ac. The combine has a swathwidth of 15 ft and the grain tank holds 250 bu.The harvesting speed is 5 mi/hr. How long does it take to fill the tank (hr)?

Grain combine harvester……

Example 6…..

An adult has approximately 1.6 x 105 km of blood vessels and a total blood volume of 4.3 L. What is the average diameter (mm) of the blood vessels? If the heart displaces approximately 65 ml per beat and beats 75 times per minute, how long (min.) is require to circulate the blood volume? What is the average velocity of blood flow in the vessels (m/sec)?

Example 7…..

A student late for class ran up the stairs in the FPAT stairway to the 2nd floor in 5 sec. The 2nd floor is 18 ft higher than the 1st floor and the student weighs 125 lb. How much power (hp) was required? What volume of gasoline (gal) would be required if the energy content of gasoline is 125,000 Btu/gal and the typical efficiency of an engine is 40%.

Example 8…..

How many acres of corn yielding 180 bu/ac will be required to fill a bin which has a diameter of 45 ft and a height of 25 ft?If the bulk density of corn is 55 lb per bushel and corn is planted in rows spaced 30 in. apart at a spacing of 10 in. between plants, what is the average mass of corn (lb) produced by each plant?