Introduction to Engineering Calculations

Process VariablesCh E 201Material and Energy BalancesObjectivesExplain the differences between density and specific gravity; the meaning of gram-mole, lb-mole, and kmol; define at least two methods for measuring temperature and pressure; the meaning of the terms absolute pressure and gauge pressure; and why atmospheric pressure is not necessarily 1 atm.Calculate density from specific gravity and vice versa.Calculate two of the quantities mass (for mass flow), volume (for volumetric flow), and moles (for molar flow) from a knowledge of the third quantity for any species of known density and molecular weight. Convert temperature units. ObjectivesGiven the composition of a mixture expressed in terms of mass fractions, calculate the composition in terms of mole fractions, and vice versa.Determine average molecular weight of a mixture from the mass or molar composition of the mixture.Convert a pressure expressed as a head of a fluid to the equivalent pressure expressed as a force per unit area, and vice versa.Convert a manometer reading into a pressure difference for an open-ended manometer, a sealed-end manometer, and a differential manometer.Mass and VolumeThe density of a substance is the mass per unit volume of that substance. The specific volume of a substance is the volume occupied by a unit mass of that substance, the inverse of the density.

Densities of pure solids and liquids are essentially insensitive to pressure, and vary relatively slightly with temperature.Mass and VolumeDensity of a pure substance can be used as a conversion factor to relate the mass and volume of a quantity of that substance. e.g., 20 cm3 of carbon tetrachloride

or 6.20 lbm of carbon tetrachloride

Mass and VolumeThe specific gravity (SG) of a substance is the ratio of the density () of the substance to the density of a reference substance at a specific condition (ref).The most common reference for solids and liquids is water at 4.0C, which has the following density:1.000 g/cm3 = 1000 kg/m3 = 62.43 lbm/ft3The density of a liquid or solid in g/cm3 is numerically equal to the SG of that substance.The notation SG = 0.6(20/4) signifies that the specific gravity of a substance a 20C with reference to water at 4C is 0.6.Mass and VolumeA thermometer uses mercury, the volume of which changes with temperature. Coefficients of linear and cubic thermal expansion of some liquids and solids are given as empirical polynomial functions of temperature in Perrys:

Flow Rate

Flow RateThe flow rate of a process stream can be expressed as a mass flow rate (mass/time) or as a volumetric flow rate (volume/time).Density can be used as a conversion factor between mass and volumetric flow rate.

The mass flow rate of n-hexane (=0.659 g/cm3) in a pipe is 6.59 g/s. What is the volumetric flow rate of n-hexane?

..

..Flow RateSuppose a gas is flowing through a cone-shaped pipe.How do the mass flow rates of the gas at inlet and outlet compare?If the density of the gas is constant, how do the volumetric flow rates at these two points compare?What if the densitydecreases from inletto outlet?

10Flow Rate MeasurementA flowmeter is a device mounted in a process line that provides a continuous reading of the flow rate in that line. Two common flowmeters are the rotameter and the orifice meter.

Chemical Compositionatomic weight weight of an atom of an element on a scale by which 12C has a mass of exactly 12. molecular weight sum of the atomic weights of the atoms that constitute a molecule of the compound.MW is a conversion factor between mass and moles for a particular compound.gram-mole the amount of that species whose mass in grams is numerically equal to its molecular weight.

Conversion: Mass/MolesConsider 8-methyl-N-vanillyl-trans-6-nonenamide, also known as capsaicin, the active component of chili peppers, having a molecular formula of C18H27NO3Calculate the molecular weight of capsaisin.

Conversion: Mass/MolesConsider 8-methyl-N-vanillyl-trans-6-nonenamide, also known as capsaicin, the active component of chili peppers, having a molecular formula of C18H27NO3Calculate the number of moles of capsaicin in 100 g of the substance

Conversion: Mass/MolesConsider 8-methyl-N-vanillyl-trans-6-nonenamide, also known as capsaicin, the active component of chili peppers, having a molecular formula of C18H27NO3Calculate the number of lbmoles of capsaicin in 100 g of the substance

Conversion: Mass/MolesConsider 8-methyl-N-vanillyl-trans-6-nonenamide, also known as capsaicin, the active component of chili peppers, having a molecular formula of C18H27NO3Calculate the number of moles each element in 100 g of the substance

Conversion: Mass/MolesConsider 8-methyl-N-vanillyl-trans-6-nonenamide, also known as capsaicin, the active component of chili peppers, having a molecular formula of C18H27NO3Calculate the number of grams of C in 100 g of the substance

Conversion: Mass/MolesConsider 8-methyl-N-vanillyl-trans-6-nonenamide, also known as capsaicin, the active component of chili peppers, having a molecular formula of C18H27NO3Calculate the number of molecules of capsaicin in 100 g of the substance

Mass and Mole Fractionsmass fraction, xA

mole fraction, yA

Conversion: Mass/Molar compositionA gas mixture of the mass composition:16% O2, 4.0% CO, 17% CO2, 63% N2 The molar composition of the gas can be found assuming a 100 g basis for calculation asiximi = xi (mtotal)Mi (g/mol)ni = mi/Miyi = ni/ntotalO20.1616 g O232 g/mol0.500 mol0.15CO0.0404.0 g CO28 g/mol0.143 mol0.044CO20.1717 g CO244 g/mol0.386 mol0.12N20.6363 g N228 g/mol2.250 mol0.69Total1.001.0x102 g3.279 mol1.00Conversion: Molar/Mass compositionA gas mixture of the molar composition:16% O2, 4.0% CO, 17% CO2, 63% N2 The molar composition of the gas can be found assuming a 100 mole basis for calculation asiyini = yi(Mtotal)Mi (g/mol)mi = ni(Mi)xi = mi/mtotalO20.1616 mol O232512 g0.16CO0.044 mol CO28112 g0.036CO20.1717 mol CO244748 g0.24N20.6363 mol N2281764 g0.56Total1.00100 mol3136 g1.00Average Molecular Weight of Mixture

ixiyiMi (g/mol)xi/MiyiMiO20.160.15320.00504.8CO0.0400.040280.00141.12CO20.170.12440.00395.28N20.630.69280.022519.32Total1.001.00(g/mol)0.032830.5

ConcentrationThe mass concentration of a component of a mixture or solution is the mass of this component per unit volume of the mixture.The molar concentration of a component of a mixture or solution is the number of moles of the component per unit volume of mixture.The molarity of a solution is the value of the molar concentration of solute expressed in gram-moles solute per liter of solution.Concentrationcan be used as a conversion factor between mass/moles of component in a sample and the volume of that sample

mass/mole flow rate of a component of a continuous stream to the total volumetric flow rate of the stream

ConcentrationParts per million (ppm), billion (ppb), trillion (ppt) are units used to express concentrations of trace species (present in minute amounts) in mixtures of gases and liquids. Units may refer to mass or molar ratios.

PressureA pressure is the ratio of a force to the area over which the force acts.

The SI pressure unit is called the pascal (Pa) which has units of N/m2. PressureFluid pressureConsider a fluid contained in a closed vessel or flowing through a pipe, and suppose a hole of area A is made in the wall of the containing vessel. The fluid pressure may be defined as the ratio of F/A, where F is the minimum force that would have to be exerted on the frictionless plug hole to contain the fluid.

Pressurehydrostatic pressureConsider a fluid contained in a vertical column. The hydrostatic pressure is based on the total force acting on the bottom of the container, and may be considered as the sum of the atmospheric pressure (Po) acting on the top of column of liquid and theweight of the column.Height h of a column is proportionalto the pressure, thus pressures may be expressed as an equivalent length, referred to as a head of liquid.

note that A does not appear in this equation, therefore the expression can be applied to any diameter liquid column28Calculating pressure from headCalculate the pressure at the at the bottom of a 12 deep swimming pool located in Las Cruces, NM in which the water temperature is a uniform 82F. Look up atmosphericpressure in Las Cruces(barometer reading 29.75 Hg)water(82F) = 62.198 lbm/ft3 Hg = 13.55 g/cm3

note the text asks to calculate head from pressure, this problem works the other direction29Absolute = Atmospheric + GaugeAbsolute pressure (psia) includes the sum of the atmospheric contribution as well as that due to the fluid acting on a particular area.Gauge pressure (psig) is that contribution from the fluid, and does not include atmospheric pressure.Consequently, a pressure of 0 psig indicates only atmospheric pressure is acting on the gauge.

note the text asks to calculate head from pressure, this problem works the other direction30Pressure measurementelastic-element methodsA Bourdon tube is C-shaped and has an oval cross-section with one end of thetube connected to the process pressure. The other end is sealed and connected to the pointer or transmitter mechanism. As pressure in the system increase, the tube tends to straighten, causing a deflection of the pointer.

Pressure measurementliquid column pressure measurement methodsLiquid column gauges consist of a vertical column of liquid in a tube whose ends are exposed to different pressures.The liquid column will rise or fall until its weight is in equilibrium with the pressure differential between the two ends of the tube.

ManometerA manometer is a U-shaped tube partially filled with a fluid of known density (the manometer fluid).Pressure at (a) and (b) is the same.

Manometer variations

Manometer CalculationA differential manometer is used to measure the drop in pressure between two points in a process line containing water. The specific gravity of the manometer fluid is 1.05. The measuredlevels in each are shown.Calculate the pressure drop between points 1 and 2 in dynes/cm2.

Manometer Calculation

TemperatureTemperature of a substance in a particular state (solid, liquid, gas) is a measure of the average kinetic energy possessed by the substance molecules.The energy cannot be directly measured, and therefore must be inferred through indirect means of a physical property of the substanceresistance thermometer (electrical resistance)thermocouple (voltage at junction of 2 dissimilar metals)pyrometer (spectra of emitted radiation)thermometer (density change of a fluid)Temperature scalesTemperatures can be expressed directly in terms of the measured physical properties (i.e., ohms/cm3).Defined temperature scales:Celsuis or Fahrenheit scales most common whjereby the scale is arbitrarily assigned two values based on the freezing (0C or 32F) and boiling (100C or 212F) points of water at 1 atm pressure.Absolute zero (lowest theoretical temperature attainable in nature) is -273.15C or -459.67F.Kelvin and Rankine are scales equivalent to Celsius and Fahrenheit, respectively, but have a value of 0 assigned to absolute zero.

Converting Temperature scalesDerived from T(B) = aT(A) + b, where temperatures represent arbitrarily assigned values of the scale.

Note the interval size oftemperature on the Fahrenheit (or Rankine)scale is 1.8 times the size of an interval on theCelsius (or Kelvin) scale.

Temperature ConversionTemperature may appear in derived units, such as the heat capacity, Cp (BTU/lbmF), which is a function of temperature. Consider Cp for ammonia:

Use a dimensional analysis approach to convert: