Konsep Dimensi dan Satuan

(Dimensions & Units)

Dr. Ir. Iwan Taruna, M.Eng

taruna©2012

Kuliah Teknologi Pengolahan 2

All engineering: deals with definite & measured quantities

Measurement: to compare the unknown with the known

The record of a measurement consists of 3 parts:

1. the dimension of the quantity2. the unit which represents a known (standard quantity) 3. number which is the ratio of the measured quantity to

the standard quantity.Contoh:

Tanaman padi tingginya 32,5 cm: Dimensi = panjang Satuan = centi meter Nilai 32,5 cm merupakan rasio tinggi padi dengan standar

satuan panjang 1 cm

DISCUSSION Dapatkah kita merancang satuan

pengukuran sendiri? Jika “YA” sebutkan syarat-syarat yg

harus dipenuhi? Berikan contoh beberapa satuan

pengukuran yang umum digunakan masyarakat tapi cenderung tidak patuh kaidah sistem British maupun SI!

ASSIGNMENT 1

Buat sebuah satuan pengukuran bahan sesuai rencana kelompok!

Buat rincian dimensi yang diukur, nama satuan yang digunakan!

Berikan deskripsi satuan yang digunakan Berikan contoh pengukurannya!

Dimensions Dimensions are represented as symbols by:

length [L] panjang mass [M] massa time [t] waktu temperature [T] suhu force [F] gaya

All engineering quantities can be expressed in terms of these fundamental Length = [L], Area = [L]2, Volume = [L]3 Dimensi turunan

Length

Mass Time

Force

Temperature

DIM ENS I TUR UNA N

Velocity = length traveled per unit time

=[L / t]

Acceleration = rate of change of velocity = [(L/t) x (1/t)] = [L / t2]

Pressure = force per unit area =[F / L2]

Density = mass per unit volume

= [M / L3] Energy = force times length

= [F x L]

Power = energy per unit time = [F x L] / t

Dimensional Consistency

All physical equations must be dimensionally consistent Dimensions can be handled algebraically and thus they

can be divided, multiplied, or cancelled Contoh:

• In the equation of motion of a particle traveling at a uniform velocity for a time t, the distance traveled is given by L = vt. Verify the dimensions of velocity.

1 tLtLvtvL ..

the dimensions of velocity must be [L][t]-1

Units (Satuan) Dimensions are measured in terms of units The units have been defined in terms of physical quantities.

the meter (m) is defined in terms of the wavelength of light; the standard kilogram (kg) is the mass of a standard lump of

platinum-iridium; the second (s) is the time taken for light of a given wavelength

to vibrate a given number of times; the degree Celsius (°C) is a one-hundredth part of the

temperature interval between the freezing point and the boiling point of water at standard pressure;

the unit of force, the Newton (N), is that force which will give an acceleration of 1 m sec-2 to a mass of 1kg;

the energy unit, the Newton meter is called the joule (J), and the power unit, 1 J s-1, is called the watt (W).

SI units: MassThe kilogram is the SI base unit of mass and is equal to the mass of the international prototype of the kilogram, a platinum-iridium standard that is kept at the International Bureau of Weights and Measures (BIPM).

The primary standard of mass for this country is United States Prototype Kilogram 20, which is a platinum-iridium cylinder kept at NIST.

Unit Consistency and Unit Conversion Unit consistency implies that the units employed for

the dimensions should be chosen from a consistent group

In this lecture we are using the SI system of units Very often, quantities are specified or measured in

mixed units. Contoh: If a liquid has been flowing at 3,5 l/min for 11,5

hours all the times have to be put into one unit only of minutes, hours or seconds before we can calculate

The SI system of units(satuan sistem SI)

Quantity Unit (satuan)

Symbol

Mass kilograms kg Length meter m Time second s Mole mole mol Temperature Kelvin K Electric current ampere A Light intensity candela cd

The SI system is an internationally agreed system of units based on seven base units.

Some derived units in the SI system

Quantity Unit Symbol

Volume Cubic meter m3

Force Newton = kg m s-2 N

Pressure Pascal = N m-2 Pa

Work, Energy Joule = N m J

Power Watt = J s-1 W

Molar concentration Molar = mol dm-3 or mol L-1 M

Multipliers for SI unit Large quantities Small Quantities

Prefix Symbol multiplier Prefix Symbol multiplier

deca D 10 deci d 10-1

hecta h 100 centi c 10-2

kilo k 103 milli m 10-3

Mega M 106 micro 10-6

Giga G 109 nano n 10-9

Tera T 1012 pico p 10-12

Exa E 1015 femto f 10-15

Unit Conversion

Conversion of 10 grams to pounds

• 1 Ib = 0.4536 kg and 1000 g = 1 kg so (1 lb/0.4536 kg) = 1 and (1 kg/1000 g) = 1.

• Therefore,

lbxkg

lbg

kggg 2102245360

11000

11010

,,

conversion factor

Dimensionless Ratios The dimensionless ratios are often used in process engineering

Contoh:• The specific gravity is a simple way to express the relative

masses or weights of equal volumes of various materials• The specific gravity (SG) is defined as the ratio of the weight

of a volume of the substance to the weight of an equal volume of water.

ww SGSG

.

Dimensionally,

13

3

LFL

FSG

Precision of Measurement Every measurement necessarily carries a degree of precision The statement of quantity should imply the tolerance

• Weight of 8.1 kg should mean that the weight lies between 8.05 and 8.149 kg better to express the limits explicitly as 8.1 ± 0.05 kg.

The temptation to refine measurements by the use of arithmetic must be resisted

Multiplication of quantities in fact multiplies errors !!!• Surface of a rectangular box is measured as 4.18 m x 2.22 m

and its depth estimated at 3 m obviously unjustified to calculate its volume as 27.8388 m3 as what arithmetic or an electronic calculator will give A more reasonable answer would be 28 m3

Contoh The thermal conductivity (k) of aluminum is

given as 120 BTU ft-1 h-1 °F-1. Calculate this thermal conductivity in J m-1 s-1 °C-1.• 1 BTU = 1055 J• 0.3048 m = 1 ft• °F = (5/9) °C.

CFx

shx

mftx

BTUJxFhftBTUk o

oo

951

36001

304801

11055120 111

/,...

-1-1-1 CsmJk o...208

Tugas 11. Konversikan nilai berikut ke satuan SI yang setara (30 poin) :

• 6,7 hp-cal/mm3 -lbf-/F• 23 g-min/cal-cm4-BTU

2. Jika viskositas minyak zaitun 5.6 x 10-2 Ib ft-1 sec-1, tentukan nilai viskositas dalam satuan SI (30 poin)

3. Bilangan Reynolds untuk aliran fluida dalam pipa adalah sbb:

Re = D.v./ dimana D diameter pipa, v kecepatan aliran fluida, densitas

fluida dan µ viskositas fluida. Dengan menggunakan 5 dimensi dasar [M], [L], [T], [F] and [t], buktikan bahwa Bilangan R adalah besaran non dimensi (40 poin)

taruna©2012Agricultural Engineering

University of Jember