Basic principles of Chemical Eng

8/18/2019 Basic principles of Chemical Eng

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Chapter One: Dimensions, Units, and Their Conversion

Objectives:

1. Understand and explain the difference between dimensions and units.

2. Add, subtract, multiply and divide units associated with numbers.

3. Specify the basic and derived units in SI and AE systems.

4. Convert one set of units in an equation into another set.

5. Apply the concepts of dimensional consistency.

6. Employ an appropriate number of significant figures.


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Dimensions: The basic concepts of measurement such as length, time, mass.

Units: Method of expressing the dimensions such as feet, centimeters.

Quantity = numerical value & units

Example : 2 meters1/3 second

2.29 kilograms

A dimension is a property that can be:

• measured such as length, mass or temperature, or

• calculated by multiplying or dividing other dimensions such as length/time(velocity).

•The two commonly used systems of units:

Units and Dimensions

AE: American Engineering system

Length = foot (ft)

Mass = pound-mass (lbm)

Temperature = Fahrenheit (F) or Rankine(R)

SI: Le Systeme Internationale d’Unities

Length = meter (m)

Mass = kilograms (kg)

Temperature = Kelvin (K) or Celsius (C)

Time = second (s)

Dimensions and their units are classified as:

Fundamental: Units that can be measured independently and defined by convention such as

grams for mass, seconds for time.

Derived: Units developed in terms of the fundamental units. They can be obtained by

multiplying or dividing fundamental units such as cubing length results in volume (liter).


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Table1.1 and 1.2: SI and AE Units

Relation between the basic and

derived dimensions


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•The distinction between uppercase and lowercase should be followed , example:

kg, K.

•They have the same form for both the singular and plural, example: 1 m, 10 m.•They are not followed by a period (except for inches, in.)

A compound unit, which is formed by multiplication of two or more other units,

consists of the symbols for the separate units joined by a dot. (example: N.m),

except in the case of familiar units such as watt-hour (Wh) and if the symbols areseparated by exponents such as N.m-2kg-2.

Unit abbreviations

Table 1.3: SI Prefixes

For SI system, units and their multiples and submultiples are related by standard

factors designated by the prefix (except for time).


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Operations with Units

•Addition and Subtraction of quantities

You can add or subtract numerical quantities only if the units are the same

5 kilograms + 3 joules10 pounds + 5 grams

•Multiplication and Division of quantities

You can multiply or divide unlike units, but cannot cancel units unless they are

identical

50 (kg)(m)/(s)

3 m2/60 cm → 3 m2/0.6 m → 5 m

The procedure for converting one set of units to another is simply to multiply any number

and its associated units by ratios termed conversion factors to arrive at the desired answerand its associated units.

Useful conversion factors can be found inside the front cover of the text book.

Conversion of units


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Examples

Convert the following number to desired units:

a) 10 cm to in.

b) 1.8 nm to dm

c) c. 42 ft2/hr to cm2/s

d) d. 1.987 cal/(gmol)(K) to Btu/(lb mol)(⁰R)


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Test Yourself:

1. Convert 1 cm/s2 to km/yr2

2. Convert 23 lbm.ft/min2 to kg.cm/s2

1lbm=0.453 kg

1m=3.281 ft


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Dimensional Consistency (Homogeneity)

A basic principle stated that equations must be dimensionally consistent, which means, each

term in an equation must have the same net dimensions and units as every other term to

which it is added, subtracted, or equated.

Consider this equation: u = u₀ + g.t

In SI system:

u(m/s) = u₀(m/s) + g(m/s2)t(s)

This equation is dimensionally homogeneous, since each of the term u, u₀,

and gt has the same dimensions (length/time)

Dimensionless GroupsDimensionless groups are used extensively in Chemical Engineering to determine relationships

between parameters, either by theory or based on experiment. They have no units.

Reynolds Number (Re):

Reynolds number is influenced by fluid properties (viscosity and density), flow conditions

(velocity) and geometry (relevant length scale). Reynolds number is the key parameter fordetermining whether flow is Laminar or Turbulent.

Re = ρVL/μ or

ρ- Density (kg/m3 in SI Units)

V - Velocity (m/s)

L - Length Scale (such as diameter of pipe) (m)

μ - Dynamic Viscosity (Pa.s) or (kg/m.s)


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Example: Dimensional Consistency

Consider the equation D(ft) = 3t(s) + 4

What are the dimensions and units of 3 and 4 ?

Derive an equation for distance in meters in terms of time in minute ?

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Test yourself: equation consistency

A crystal of diameter D (mm) is placed in a solution of dissolved salt, and new crystals are formed at a

constant rate r (crystals/min). Experiments show that the rate of crystal formation varies with the

crystal diameter as:

r ( crystals/min)= 200 D-10D2

(D in mm)

a) What are the units of the constants 200 and 10?

b) Calculate the crystal formation rate in crystal/s for a crystal diameter of 0.050 in.

c) Derive a formula for r (crystals/s) in terms of D( inches).

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Test yourself: Dimensionless Groups

Calculate the Re for the following set of conditions for a fluid flowing in a pipe:

Re = ρVD/ μ

– ρ- Density = 62.3 lb/ft3 (AE)

– V - Fluid Velocity = 2 m/s (SI)

– D - Pipe Diameter = 2 in. (AE)

– μ - Viscosity = 2.5 g/cm.s (SI)

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ForceAccording to Newton’s 2nd Law of Motion, force is proportional to the product of mass and

acceleration (length/time2), F= m.a

In the SI system, the unit of force is defined to be the Newton (N) when 1 kg is accelerated

at 1 m/s2 .

1 newton (N) ≡ 1 kg.m/s2

F= Cma 1N 1kg 1 m

In the American engineering system, the derived force unit is called a pound-force (lbf ) and

is defined as the product of a unit mass (1 lbm) and the average acceleration of gravity at

sea level at 45 ̊latude, which is 32.174 ft/s2

(depending on the location of the mass)

1 lbf ≡ 32.174 lbm.ft/s2

F= Cma = 1 lbf 1 lbm g ft = 1 lbf

32.174 lbm

.ft /s2 s2

m = 1 kga = 1 m/s2

F = 1 N

m = 1 lbma =g= 32.174 ft/s2

F = 1 lbf

(kg)(m)

s2s2

= 1N → C= 1 Nkg.m

s2

gc = 1/C= 1 kg.m/s2 = 32.174 ft.lbm/s

2

1 N 1 lbf

=

Conversion factor


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Weight

The weight of an object is the force exerted on the object by

gravitational attraction. W = m.g

The value of g at sea level and 45° latitude for each system of unitsis: g = 32.174 ft/s2 (AE)

= 9.8066 m/s2 (SI)

Example: weight

Water has a density of 62.4 lbm/ft3. How much does 2 ft3 of water weigh (1) at sea level

and 45 ̊latude and (2) in a location where the attitude is 5374 ft and the gravitationalacceleration is 32.139 ft/s2?

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Test yourself: Mass and Weight

A waste treatment pond is 50 m long and 15 m wide, and has an average depth of 2

m. The density of the waste is 85.3 lbm/ft3. Calculate the weight of the pond

contents in lbf .

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The Importance of Proper Units

Mars Climate Orbiter

SEPTEMBER 30, 1999

Likely Cause Of Orbiter Loss Found

The peer review preliminary findings indicate that one team used English

units (e.g., inches, feet and pounds) while the other used metric units for a

key spacecraft operation.

Gimli Glider is the nickname of an Air Canada aircraft which was involved in an infamous aviation incident. On 23 July 1983, a Boeing

767-200 jet, Air Canada Flight 143, ran completely out of fuel at 41,000 feet (12,500 m), about halfway through its flight from Montreal to

Edmonton. The subsequent investigation revealed that fuel loading was miscalculated through misunderstanding of the recently adopted

metric system which replaced the Imperial system. At 41,000 feet, over Red Lake, Ontario, the aircraft's cockpit warning system sounded,

indicating a fuel pressure problem on the aircraft's left side. Assuming that a fuel pump had failed, the pilots turned it off, as gravity would

still feed fuel to the aircraft's two engines. The aircraft's computer indicated that there was still sufficient fuel for the flight, but, as

subsequently realized, the calculation was based on incorrect settings. A few moments later, a second fuel pressure alarm sounded,

prompting the pilots to divert to Winnipeg. Within seconds, the left engine failed and they began preparing for a single-engine landing. As

they communicated their intentions to controllers in Winnipeg and tried to restart the left engine, the cockpit warning system sounded

again, this time with a long "bong" that no one present could recall having heard before. This was the "all engines out" sound, an event

that had never been simulated during training. Seconds later, most of the instrument panels in the cockpit went blank as the right-side

engine also stopped and the 767 lost all power. At this point, the pilot proposed his former airforce base at Gimli as a landing site.

Unknown to him, however, the base had become a dragstrip and had decommissioned one of its runways. As a result of the runway's

conversion to use as a dragstrip, the runway had been converted into two lanes with a guard rail running down the middle of it.

Furthermore, a "Family Day" was underway at the dragstrip that particular day and the area around the decommissioned runway was

covered with cars and campers. The decommissioned runway itself was being used to stage a race. As soon as the wheels touched the

runway, the pilot "stood on the brakes“, blowing out two of the aircraft's tires. The unlocked nose wheel collapsed and was f orced back

into its housing, causing the aircraft's nose to scrape along the ground. The plane slammed into a guard rail which made the plane lose a

bit more speed to stop it from flying off the runway. None of the 61 passengers was

seriously hurt during the landing.

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Basic principles of Chemical Eng