Units and Dimensions. 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. Mars Climate Orbiter.
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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.
Mars Climate Orbiter
Units and Dimensions
Quantity = numerical value & units
Example - 100 kg/hr
Dimensions = basic concepts of measurement
Units = quantitatively expressing dimensions
All dimensions of interest can be expressed in terms of:
What are the dimensions & (SI units) on the following ?
L/t2 (m/sec2 )
M*L/t2 (Kg m/ sec2)
M/L*t2 (Kg m / m2 sec2)
M*L2/t2 Kg m2 / sec2)
Typically, coefficients in physical laws (eg, KE = ½ mv2),exponents, and arguments (log x, sin x, exp x = ex) have no dimensions.
There are special dimensionless numbers used in chemical
engineering; for example:
Dimensional Homogeneity & Dimensionless Numbers
• every added and subtracted term in any equation must have the same dimensions.
Multiplication & Division of quantities
• creates compound dimensions and units
Addition and Subtraction of quantities
• must have same dimensions & units
Consider the equation D(ft) = 3t(s) + 4
• What are the dimensions and units of 3 and 4 ?
Convert the equation D(ft) = 3t(s) + 4 to D’(m) = __t’(min) + __
Convert each term then substitute ...
D(ft) = D’(m) * 3.2808 ft / m & t(s) = t’(min) 60 s / min
Thus, 3.2808D’(m) = 3*[60 t’(min)] + 4
D’(m) = 55t’(min) + 1.22
• What are the dimensions & units of 55 and 1.22 ?
You are traveling at 51 km/hr and increase your speed
by 1 ft/s; what is your new velocity?
Can you add these because they have the same dimensions ?
Dimensional ledger/ equations
• think units first, then numerical values
• break big problem down
Problem Set Handout: I-1 – I-17
Mass: amount of material - mass ≠ weight
Weight: Force that material exerts due to gravity (g) which changes with location, etc.
Force: (Newton, dyne, or lbf) = mass * acceleration (F = m *a)
Mass = kg (SI), g (CGS), or lbm (English)
Momentum (lbf) is equal to mass (lbm / sec) X velocity (ft/sec)
Determine the momentum force transferred to a wall by a stream of
water flowing from a fire hose at 50 ft/sec and 1000 lb/hr.
Problem Set Handout: I-18 – I-21
Mole = certain number of entities
6.023 X 1023 molecules
• g-mole = amt of substance whose mass in grams is
equal to the molecular weight of the substance
• similarly kg-mole & lb-mole
• molecular weight (MW) =
• atomic weight - atomic mass .... Inside back cover of textbook
Silver nitrate (lunar caustic) is a white crystalline salt, used in marking inks, medicine and chemical analysis. How many kilograms of silver nitrate (AgNO3) are there in :
a. 13.0 lb mol AgNO3.
b. 55.0 g mol AgNO3
Calcium carbonate is a naturally occurring white solid used in the manufacture of lime and cement. Calculate the number of lb mols of calcium carbonate in:
a. 50 g mol of CaCO3.
b. 150 kg of CaCO3.
c. 100 lb of CaCO3.
Tabulated Specific Gravities
Example: SG of Ethanol at 140 F
The density of a liquid is 1500 kg/m3 at 20°C.
occupy at 20°C ?
A liquefied mixture of n-butane, n-pentane and n-hexane has the following composition in weight percent.
n - C4H10 = 50 %
n - C5H12 = 30 %
n - C6H14 = 20 %
Calculate the weight fraction, mol fraction and mol percent of each component and also the average molecular weight of the mixture.
A mixture of gases is analyzed and found to have the
following composition (volume percent). How much will
3 lb mol of this gas weigh ?
Concentration = quantity of A / volume
kg / m3 kg mol / m3 g/L g /cc
lb / ft3 lb mol / ft3
A solution of HNO3 in water has a specific gravity of 1.10 at 25 C. The concentration of HNO3 is 15 g/L.
What is the mole fraction of HNO3 in the solution ?
What is the ppm (wt) of HNO3 in the solution ?
The 1993 Environmental Protection Agency (EPA) regulation contains standards for 84 chemicals and minerals in drinking water. According to the EPA one of the most prevalent of the listed contaminants is naturally occurring antimony. The maximum contaminant level for antimony and nickel has been set at 0.006 mg/L and 0.1 mg/L respectively.
A laboratory analysis of your household drinking water shows the antimony
concentration to be 4 ppb (wt) (parts per billion) and that of nickel to be 60 ppb (wt).
Determine if the drinking water is safe with respect to the antimony and nickel levels. Assume density of water to be 1.00 g/cm3
Problem Set Handout: I-22 – I-44
Temperature - average kinetic energy of molecules.
Rankin ( °R )
T (°K) = T (°C ) + 273.15
T (°R) = T (°F ) + 459.67
T (°R) = T (°K ) * 1.8
DT ≠ T - conversions approaches are different
Given the following equation:
Problem Set Handout: I-45 – I-51
Pressure is defined as the amount of force exerted on a unit area of a substance:
Pipe or tube
Pressure is a Normal Force
(acts perpendicular to surfaces)
It is also called a Surface Force
33.91 ft of water (ft H20)
14.696 psi (lbf / in2)
29.92 in Hg
760 mm Hg
1.013 X 105 Pascal (Pa)
A force balance in the z direction gives:
For an infinitesimal element (Dz0)
Liquids are incompressible i.e. their density is assumed to be constant:
When we have a liquid with a free surface the pressure P at any depth below the free surface is:
Po is the pressure at the free surface (Po=Patm)
By using gauge pressures we can simply write:
Apply the basic equation of static fluids to both legs of manometer, realizing that P2=P3.
A U-tube manometer is used to determine the pressure drop across an orifice meter. The liquid flowing in the pipe line is a sulfuric acid solution having a specific gravity (60°/60°) of 1.250. The manometer liquid is mercury, with a specific gravity (60°/60°) of 13.56. The manometer reading is 5.35 inches, and all parts of the system are at a temperature of 60°F.
What is the pressure drop across the orifice meter in psi ?
The barometric pressure is 720 mm Hg. The density of the oil is 0.80 g/cm3 . The density of mercuryis 13.56 g/cm3 The pressure gauge (PG) reads 33.1 psig. What is the pressure in kPa of the gas ?
Problem Set Handout: I-52 – I-63