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