zahid unit dan dimensi
DESCRIPTION
Punya Zahid, Kuliah TPHP 1, THP44TRANSCRIPT
UNIT DAN DIMENSI
1
DIMENSI
Suatu gambaran jenis dari kuantitas fisik
Contoh:
- Panjang - gaya- luas - massa- volume - kecepatan- waktu - suhu
- dan lain-lain
2
UNIT
Sesuatu yang digunakan untuk menyatakan ukuran atau kuantitas dari suatu dimensi
Ada bermacam-macam SISTEM UNIT yang digunakan :
- British Unit
- American Unit
- Engineering Unit
-Yang umum digunakan adalah Unit SISTEM
INTERNASIONAL (SI) 3
4
Some Tools for Measurement
5
Standard Kilogram at Sèvres
SISTEM PENGUKURAN
SYSTEM USEDIMENSI
LENGTH MASS TIME TEMP FORCE ENERGY
ENGLISH ABSOLUTE
scientific foot (ft) Pound mass (lbm)
sec. °F Poundal BTU ft (pou-ndal)
BRITISH ENG.
INDUSTRI foot (ft) slug sec. °F pound force (lbf)
BTU ft (lbf)
AMERICAN ENG.
US. INDUSTRY
foot (ft) pound mass (lbm)
sec. °F lbf BTUft (lbf)
METRIC
CGS Scientific cm gram sec °C dyne Calori, erg
MKS industri m kg sec °C kgf Kilocalori, joule
SI universal m kg sec °C newton joule
6
Unit Dasar
7
QUANTITY UNIT NAME
UNIT DIMENSIONS
Basic UnitMass Kilogram kg MLength, Diameter Meter m LTime Second s TTemperature Kelvin K θ
Unit turunan
8
QUANTITY UNIT NAME
UNIT DIMENSIONS
Derived unit with a special nameForce Newton (N) kg m s-2 MLT-2
Pressure Pascal (Pa) Nm-2 ML-1T-2
Energy Joule (J) Nm ML2T-2
Power Watt (W) Js-1 ML2T-3
Frequency Hertz (Hz) Hz T-1
Absorbed dose of ionising radiation
Gray (Gy) Jkg-1 L2T-2
Unit turunan
9
QUANTITY UNIT NAME
UNIT DIMENSIONS
Derived unit without a special nameArea m2 L2
Volume m3 L3
Density kgm-3 ML-3
Dynamic viscosity N s m-2 ML-1T-1
Kinematic viscosity M2s-1 L2T-1
Enthalpy Jkg-1 L2T-2
Specific heat Jkg-1K-1
(or oC)LT-2θ-1
TEHNIK KONVERSI
10
Ada beberapa cara untuk mengkonversi dari unit yang
satu ke unit yang lain, dalam satu sistem atau antar
sistem :
1.Dengan Tabel
2. Dengan simbol Prefix
3. Dengan menghitung
Tabel Konversi
11
QUANTITY BRITISH SYSTEM SILength 1 ft 0,3048 mTime 1 h 3,6 ksArea 1 ft2 0,09290 m2
Volume 1 ft3 0,02832 m3
Mass 1 lb 0,4536 kgDensity 1 lb ft-3 16,019 kg m-3
Force 1 lbf 4,4482 NEnergy 1 Btu 1055,1 J
1 cal 4,1868 JPressure 1 lbf in-2 6894,8 Pa
1 atm 1,0133 x 105 Pa1 torr 133,32 Pa
Power 1 Btu h-1 0,29307 W1 hp 745,70 W
Velocity 1 ft s-1 0,3048 m s-1
Dynamic viscosity 1 P (poise) 0,1 N s m-2
Kinematic viscosity 1 St (stokes) 10-4 m2 s-1
Specific heat 1 Btu lb-1 oF-1 4,1868 kJ kg-1 K-1
Thermal conductivity 1 Btu h-1 ft-1 oF-1 1,7303 W m-1 K-1
Heat transfer coefficient 1 Btu h-1 ft-2 oF-1 5,6783 W m-2 K-1
Mass transfer coefficient 1 lb ft-2 s-1 1,3563 g m-2 s-1
Temperature oF oC95
Sistem konversi dengan PREFIX
12
PREFIX MULTIPLE SIMBOLTERA 1012 TGIGA 109 GMEGA 106 MKILO 1000 (103) kMILLI 10-3 m
MICRO 10-6 μNANO 10-9 nPICO 10-12 p
FEMTO 10-15 f
13
SI System of UnitsForce = (mass) (acceleration)
SI System of Units: Force
Force = ma
= Newton = N
2smkg
SI System of Units: Stress/Pressure
Pressure = Force / Area
= Pascal = Pa
2
2
2 ms/mkg
mN
2smkg
16
U.S. Customary System of Units (USCS)
Fundamental Dimension Base Unit
length [L]
force [F]
time [T]
foot (ft)
pound (lb)
second (sec)
Derived Dimension Unit Definition
mass [FT2/L] slug lbf sec2/ft
USCS: Force = (mass)*(acceleration)
2f ft/secslug1lb1
F = ma
W = mg
American Engineering System Note, there is a problem when we use the
same unit (“pound”, meaning lbf and lbm) to describe two different dimensions.
Newton's Second Law: F = ma 1 lbf = 1 lbm ft/s2 ??? NO!!!
Must have consistency of units.
Consistency of Units Principle of consistency of units:
units on the left side of an equation must be the same as those on the right side of an equation
dimensional homogeneity
AES and Newton’s Law
Must maintain dimensional homogeneity:
Now we have lbf = lbf
cgmaF
2f
mc sec lb
ftlb32.174
g
KONSTANTA DIMENSIONAL (gc)
21
Muncul karena adanya gaya gravitasi bumi
1 lb dalam berat diatas permukaan bumi disebabkan oleh :
1 lb massa yang dipengaruhi oleh gaya gravitasi
2sec1 ftxlblb mf
22
xftxlblb mf 2sec Dimensional konstan
Cmf g
xftxlblb 1sec2
2secf
mc lb
ftlbg
Untuk menghasilkan konsistensi dalam unit
dibutuhkan konstanta
Gravitasi bumi = 2sec174,32 ft
2sec174,32
f
mc lb
ftlbg
23
Force and Weight
Be sure you understand the difference between lbf and lbm
Be sure you understand the difference between the physical constant g, and the conversion factor gc.
24
FORCE, WEIGHT AND MASS Force is proportional to product of mass and
acceleration and is defined using derived units to equal the natural units;
1 Newton (N) = 1 kg.m/s21 dyne = 1 g.cm/s21 Ibf = 32.174 Ibm.ft/s2
Weight of an object is force exerted on the object by gravitational attraction of the earth i.e. force of gravity, g.
To convert a force from a derived force unit to a natural unit, a conversion factor, gc must be used.
A ratio of gravitational acceleration, g to gc may be used for most conversions between mass and weight.
25
FORCE, WEIGHT AND MASS
1. F = ma /gc : W = mg /gc kg.m/s2 g.cm/s2 Ibm.ft/s2 2. gc = 1 --------- = 1 --------- = 32.174 ----------- N dyne Ibf 3. g = 9.8066 m/s2 ===> g/gc = 9.8066 N/kg g = 980.66 cm/s2 ===> g/gc = 980.66 dyne/g g = 32.174 ft/s2 ===> g/gc = 1 Ibf/Ibm 4. Example: Water has a density of 62.4 Ibm/ft3. How much does 2.000 ft3 of water weigh?
Dimensional Analysis
Dimensions & units can be treated algebraically.
Variable from Eq.
x m t v=(xf-xi)/t
a=(vf-vi)/t
dimension L M T L/T L/T2
Dimensional AnalysisChecking equations with dimensional analysis:
L(L/T)T=L
(L/T2)T2=L
• Each term must have same dimension• Two variables can not be added if dimensions
are different• Multiplying variables is always fine• Numbers (e.g. 1/2 or p) are dimensionless
x f xi vit 12at 2
Example 1.1
Check the equation for dimensional consistency:
22
2
)/(1mc
cvmcmgh
Here, m is a mass, g is an acceleration,c is a velocity, h is a length
Example 1.2
L3/(MT2)
Consider the equation:
Where m and M are masses, r is a radius andv is a velocity.What are the dimensions of G ?
mv2
rG
Mmr2
Example 1.3Given “x” has dimensions of distance, “u” has dimensions of velocity, “m” has dimensions of mass and “g” has dimensions of acceleration.
Is this equation dimensionally valid?
Yes
Is this equation dimensionally valid?
No
x (4 / 3)ut
1 (2gt 2 / x)
x vt
1 mgt 2
Units vs. Dimensions
Dimensions: L, T, M, L/T … Units: m, mm, cm, kg, g, mg, s, hr, years … When equation is all algebra: check
dimensions When numbers are inserted: check units Units obey same rules as dimensions:
Never add terms with different units Angles are dimensionless but have units
(degrees or radians) In physics sin(Y) or cos(Y) never occur
unless Y is dimensionless
32
Example The density of a fluid is given by the empirical
equation
ρ = 1.13 exp(1.2 x 10-10 P)Where ρ = density in g/cm3
P = pressure in N/m2
a) What are the units of 1.13 and 1.2 x 10-10?b) Derive the formula for r(lbm/ft3) as a function of P (lbf/in2)
A column of mercury is 3 mm in diameter x 72 cm high. If the density of mercury is 13.6 g/cm3, what is its weight in N. What is its weight in lbf? What is its mass in lbm?
33
Example The Reynolds number is the dimensionless
quantity that occurs frequently in the analysis of the flow of fluids. For flow in pipes it is defined as DVρ/μ, where D is the pipe diameter, V is the fluid velocity, ρ is the fluid density, and μ is the fluid viscosity. For a particular system having D = 4.0 cm, V = 10.0 ft/s, r = 0.700 g/cm3, and μ = 0.18 centipoise (cP) (where 1 cP = 6.72 x 10-4 lbm/ft.s). Calculate the Reynolds number.