Lecture 4 - Units & Engineering Calculations

What does pico mean and what is its symbol?

0.000 000 000 001 times = 10^-12 pico = p It means that the unit, for example grams, is multiplied by 0.000 000 000 001 (picograms).

What does nano mean and what is its symbol?

0.000 000 001 times = 10^-9 nano = n It means that the unit, for example grams, is multiplied by 0.000 000 001 (nanograms).

What does micro mean and what is its symbol?

0.001 000 times = 10^-6 micro =u It means that the unit, for example grams, is multiplied by 0.001 000 (micrograms).

What does milli mean and what is its symbol?

0.001 times = 10^-3 milli =m It means that the unit, for example grams, is multiplied by 0.001 (milligrams).

What does centi mean and what is its symbol?

0.01 times = 10^-2 centi =c It means that the unit, for example grams, is multiplied by 0.01 (centigrams).

What does deci mean and what is its symbol?

0.1 times = 10^-1 deci =d It means that the unit, for example grams, is multiplied by 0.1 (decigrams).

What does kilo mean and what is its symbol?

1,000 times = 10^3 kilo =k It means that the unit, for example grams, is multiplied by 1,000 (kilograms).

What does mega mean and what is its symbol?

1,000,000 times = 10^6 mega =M It means that the unit, for example grams, is multiplied by 1,000,000 (gigagrams).

What does giga mean and what is its symbol?

1,000,000,000 times = 10^9 giga =G It means that the unit, for example grams, is multiplied by 1,000,000,000 (megagrams).

Define dilution factor

ask lecturer

What are equations in terms of physical variables?

"Properly construted" equations represent general relationships between physical variables. They must be dimensionally homogenous

Name one of the most common natural variables used by biochemial engineers, descirbe what it is and give its general formula

- A particularly important dimensionless number for biochemical engineers is Reynolds number. - In fluid mechanics, the Reynolds number (Re) is a dimensionless number that gives a MEASURE OF THE RATIO OF INERTIAL FORCES TO VISCOUS FORCES for GIVEN FLOW CONDITIONS. The Reynolds number is an important parameter that DESCRIBES WHETHER THE FLOW CONDITIONS LEAD TO LAMINAR OR TURBULENT FLOW. It is used both for pipeline flow and stirred tanks (among other things)

How do you convert between units? What is the general method?

- Good way to do it, is to cancel out your units. For example: What is 120 L min^-1 in m^3 s^-1 Find out what the given units are converted into the units you need. So 1 min = 60 secs and 1 L = 1000m^3. Then multiply the given value with the conversions so that the units cancel out, giving you your asnwer in the needed units.

Is number of rotations (expressed in radians or revolutions) a dimensionless variable? Why or why not? Hence, what dimensions does rotational speed have?

- In calculations involving rotational phenomena, rotation is described based on the number of radians or revolutions. In the formulas, r is radius. - One revolution is equal to 2xpie radians. Radians and revolutions are non-dimensional because the dimensions of length for arc, radius, and cricumference in eqs. 2.2. and 2.3 cancel. - Consequently, rotational speed (e.g. number of revolutions per second) and angular velocity (e.g. nuber of radian per second) have dimensions T^-1.

What are alternative names for natural variables?

- Natural variables - dimensionless variables (dimensions are the SI symbols for the specific base quantities, i.e. the units of the physical quantity). - dimensionless groups - dimensionless numbers

Define substantial variables

- One of the two main types of physical variables - Substantial variables have: 1. Magnitude (physical variables can be quantified by measurement) 2. Units (expression of the magnitude of substantial variables requires a PRECISE PHYSICAL STANDARD against which measurement is made > e.i. UNITS) >> Statements about the magnitude of substantial variables must contain these 2 parts (the number and the unit used for measurement). Reporting the magnitude of a substantial variable has no meaning without information about the units. E.g. a car has speed 20, is meaningless without the unit of km per hour.

Is it important to be able to convert between units and why?

- Several systems of units for expressing the magnitude of physical variables have been devised through the ages. - Despite widespread use of SI units, no single system of units has universal application. In particular, engineers in the US continut to apply the Britsih or imperial units. In addition, many physical property, data collected befpre 1960 (when SI was agreed upon) are published in lists and tables using nonstandard units. - Therefore, familiarity with both metric and nonmetric units is necessary.

Define natural variables

- The second group of physical variables (PROPERTY of a body or substance that can be QUANTIFIED BY MEASUREMENT) are natural variables. Natural variables have: 1. Magnitude (physical variables can be quantified by measurement) BUT 2. Do NOT require units or any other standard of measurement. Unlike substantial variables, natural variables are still meaningful without units.

What is the general formula for the Reynolds number?

- The specific calculation of the Reynolds number, will depend on the geometry of the flow system and flow pattern. But the general formula is: Ref = (inertial forces)/(viscous forces)

Given a fermenter of particular dimensions, what variable(s) can you change to achive different flow types (laminar, turbulent or transitional)?

- The variables of the equation for Rei -Impeller diameter has the greatest effect on fluid flow, because the variable is sqaured in the equation. So this would be the easiest variable to change. - Liquid density, for example density of the medium could be changed - Viscosity and rotational speed could also be changed.

Is it only necessary to convert between imperial and metric units?

- Unit conversions are not only necesarry to convert imperial units to metris; - Some physical variables have several metric units in common use. - For example, viscocity may be reported as centipose or kg h^-1 m^-1.

Define conversion factors

- Used to change units. An arithmetical multiplier for converting a quantity expressed in one set of units into an equivalent expressed in another. A numerical factor used to multiply or divide a quantity when converting from one system of units to another (the factor should be arranged, such that the units cancel out).

How can substantial variables be manipulated?

1. Added or subtracted: - Values of two or more substantial variables may be added or subtracted, ONLY IF THEIR UNITS ARE THE SAME. E.g. 5kg + 2kg = 7kg But 4kg + 8Pa does not mean anything. 2. Multiplied or divided: - Values and units of ANY substantial varibles can be combined by multiplication or division, but their UNITS MUST BE COMBINED. E.g. 60mph, 5ms^-1 (>>> Derived variables)

What are the general steps for producing a buffer in a lab?

1. Calculate all concentrations in mol/l (for M) or g/l as appropriate 2. Decide whether a stock solution is used (a) or the substances need to be weighed in (b) 3.Calculate the volumes of the stock solutions (case a) or the amounts to be weighed (case b) 4.) Think about the results - are they plausible? (If you need to weigh in tons or picograms of something there is something wrong). 5.) Weigh in all the substances/add the correct volumes of all necesary sotck solutions 6.) Fill up your solution with the appropriate solvent 7.) Dpending on the solution: Adjust pH.

What are derived quantities and derived units?

1. Derived quantities are physical quantities which are derived from the base quantities by multiplication or division or both. For example, speed is a derived quantity of length (distance travelled) over time. (ALL OTHER QUANTITIES, THAT ARE NOT BASE QUANTITIES, ARE DERIVED QUANTITIES). 2. Derived units are units of measurements (for derived quantities) which are derived from base units of the component base quantities by multiplication or division or both. In the case of the derived quantity, speed, its derived unit is metre/time (with unit symbol, m/s or ms-1).

What are the two main types of natural variables?

1. Simplest natural variables: are ratios of substantial variables with the same dimensions. For example, the aspect rator of a cylinder is its legnth divide by its diameter; the result is a dimensionless number. 2. More complex natural variables: Ratios that involve a combination of substantial variables that do not have the same dimensions (but still some of the same, to cancel each other out).

Objectives of Lecture: 1. Understand physical variables, dimensions and units 2. Be familiar with SI units commonly found in science and engineering 3. Be able to convert between units 4. Understand how to perform common science and engineering calculations

1. Understand physical variables, dimensions and units 2. Be familiar with SI units commonly found in science and engineering 3. Be able to convert between units 4. Understand how to perform common science and engineering calculations

Is the following a "proper equation": y = A sin (w (t - (x/v)), where A is amplitude, frquency w/2xpie and veolicty v, t is time and x is distance from the origin.

1.) Dimensions of both sides of the equation are the same (dimensionless) 2.) Dimensions that are subtracted are the same (T) 3.) Argument inside the transcedental function is dimensionless w (t - (x/v) = T^-1 (T - L / (L/T)) = T^-1 (0). = 0 = dimensionless. Therefore it fulfills all 3 criteria for a proper equation

What does deca mean and what is its symbol?

10 times = 10^1 deca =da It means that the unit, for example grams, is multiplied by 10 (decagrams).

What does hecto mean and what is its symbol?

100 times = 10^2 hecto =h It means that the unit, for example grams, is multiplied by 100 (hectograms).

Define buffer solution

A buffer is a solution containing either a weak acid and its salt or a weak base and its salt, which is resistant to changes in pH. Some solutions resist changes in pH when small amounts of acid or base are added. On addition of acid the hydrogen ions get removed by one of the components of the mixture and on addition of base the hydroxide ions get removed by one of the components of the mixture. The effect is called buffering action an solutions that behave this way are called buffers.

Discuss laminar fluid flow across a cross section of a pipe

A common application of laminar flow is in the smooth flow of a viscous liquid through a tube or pipe. In that case, the velocity of flow varies from zero at the walls to a maximum along the cross-sectional centre of the vessel In other words: Laminar flow can be regarded as a series of liquid cylinders in the pipe, where the innermost parts flow the fastest, and the cylinder touching the pipe isn't moving at all.

What is the mass percent or weight-for-weight percent a measure of? How is it calculated? What is the unit symbol given? What is it used for?

A measure of concentration = abundance of a constituent divided by the total volume of a mixture. - Mass percent is: Concentration = ((mass of A) / (total mass)) x 100. Units is % For example, a solution of sucrose in water with a concentration of 40% w/w contains 40 g sucrose per 100 g solution. This is used for solids dissolved in liquids.

What is the amount per volume a measure of? How is it calculated? What is the unit symbol given? What is it used for?

A measure of concentration = abundance of a constituent divided by the total volume of a mixture. Concentration (c) = amount (n) / volume (V) c = n/V mol/l = M. Symbol is capital M. Used for salts, buffer concentrations etc. Calculation in which it is easy to calculate the relative molecular mass, so that number of moles (n = mass/Mr) can easily be calculated.

What is the mass per volume a measure of? How is it calculated? What is the unit symbol given? What is it used for?

A measure of concentration = abundance of a constituent divided by the total volume of a mixture. Concentration (c) = mass (m) / volume (V) c = m/V g/l = unit. Used for proteins, DNA RNA concentrations (mg/ml or ug/ul). Calculation in which it is not easy to calculate the relative molecular mass, so that number of moles (n = mass/Mr) cannot easily be calculated, and so it is easier to use grams/volume instead.

What is the volume per volume percent a measure of? How is it calculated? What is the unit symbol given? What is it used for?

A measure of concentration = abundance of a constituent divided by the total volume of a mixture. volume concentration conc. = (volume of constituent / volume of mixture) x 100 c = (V1/V2) 100 % Used for liquids dissolved in liquids (e.g. detergents).

Define metric prefix. Give an example

A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or fraction of the unit. E.g. kilogram is a 1000 grams. Allows us to conceptualize very small and larger numbers quickly.

Define physical variable

A physical variable is a PROPERTY of a body or substance that can be QUANTIFIED BY MEASUREMENT e.g. length, velocity, viscosity. There are two main types of physical variables: 1. Substantial variables 2. Natural variables

Define stock solution

A stock solution is a large volume of a common reagent, such as hydrochloric acid or sodium hydroxide, at a standardized concentration. A Stock Solution is a CONCENTRATED SOLUTOIN that will be DILUTED to some lower concentrated for actual use. >> Stock solutions are used toSAVE PREPARATION TIME, CONSERVE MATERIALS, REDUCE STORAGE SPACE, and IMPROVE ACCURACY with which working solutions are prepared.

Are all derived quantities denoted using their derived units? Give examples.

All base units are denoted using their base units. However, some, often used physical quantities, have derived units that cumbersome to write out, and have been given special names/abbreviations by SI.

Define concentration

Concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: 1. mass concentration, (conc. = mass / volume) 2. molar concentration (conc. = moles / volume) 3. number concentration (conc. = # of entities / volume) 4. volume concentration (conc. = volume of constituent / volume of mixture).

Discuss density. Definition What kind of variable is it? Dimensions symbol

Density is a substantial variable defined as mass per unit volume. Its dimensions are L^-3M Common symbol is p (in cursiv) SI units for density is kg/l (it is a derived quantity). Other units used for density: g cm^-1, kg m^-3 and lb ft^-3.

Define dimensionally homogenous

Describes/is a property of equations. - For dimensional homogeneity: 1.) The DIMENSIONS of terms that are ADDED/SUBTRACTED must be the SAME 2.) The DIMENSIONS of the RIGHT SIDE of the equation must be the SAME as those on the LEFT SIDE 3.) The argument of any transcendental function, such as a logarithmic, trigonometric, or exponential function, must be dimensionless (the stuff that is inside the log bracks, log(dimensionless), must be dimensionless).

What are dimensional symbols and unit symbols?

Dimensional symbol: the 1 roman letter symbol (lower case, except for base quantities arising from names) given as a short hand for a base quantity Unit symbol: The symbol given to represent the unit of the physical quantity being measured.

What are base quantities also called?

Dimensions: For example the base quantity Time, has been given dimension symbol T. The base quantities are called dimensions, from which the dimensions of other physical varibles are derived. THey are very useful for claculations, because the dimensions of physical quantity remains the same, the units are not important/irrelevant.

What is engineering calculations all about?

Engineering calculations involve manipulation of numbers. Most of these numbers represent the magnitudes of measurable physical variables, such as mass, length, time and velocity.

What do engineers often use natural variables for?

Engineers make frequent use of dimensionless numbers for succinct (briefly or clearly expressed) representation of physical phenomena. For example a common dimensionless group in fluid mechanics is the Reynolds number, Re.

What is the most important dimensionless group/variable for stirred tanks? Give its equation.

For stirred tanks the most important dimensionless group is also the Reynolds number

What has been developed to ensure there are no misunderstandings of the units?

Formally agreed in 1960 · To overcome the difficulty, the SI (International System of Units) has CHOSEN AND STANDARDIZED UNITS OF MEASUREMENT for all PHYSIVAL QUANTITIES - The CHOSEN UNITS OF MEASUREMENT are known as the SI (abbreviated as SI, from the French Système international (d'unités)) units. SI has recognized some physical quantities as base quantities and others as derived quantities

What is the dimension for frequency

Frequency = #of completed cycles/T Number of completed cycles has no dimension (it is not a physical quantity, but a number) Thus dimension of Frequency = T^-1

Define base quantities

In a system of measurement base quantities are: - A SUBSET of PHYSICAL QUANTITIES - CHOSEN & ARBITRARILY DEFINED, rather than being derived from a combination of other physical quantities. - FUNDAMENTAL PHYSICAL QUANTITIES that are NOT DEFINED IN TERMS OF OTHER PHYSICAL QUANTITIES and upon which other physical quantities - known as derived quantities - are derived. The following physical quantities, units and symbols are chosen by the SI (International System of Units) as base quantities, base units and unit symbols:

Define dimensionless analysis

In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric charge) and units of measure (such as miles vs. kilometers, or pounds vs. kilograms vs. grams) and tracking these dimensions as calculations or comparisons are performed. "A method for comparing the dimensions of the physical quantities occurring in a problem to find relationships between the quantities without having to solve the problem completely." Biochemical engineering problems are determined by complex interactions between: 1. Equipment design 2. Operating conditions 3. Physical properties of liquid being processed i.e. several variables are invovled. In these^cases we use an engineering approach called DIMENSIONLESS ANALYSIS to relate the most important variables together in the form of dimensionless groups (or numbers) **It is not neccesry to go into principles of dimensionless analysis here. Rather, it is only necessary to realise that they represent groupings of the most important variables in the process.

In the past, has there been agreed upon units for specific substantial variables? Discuss issues with this. Give examples.

In the past, for the SAME PHYSICAL QUANTITY, DIFFERENT UNITS OF MEASUREMENT WERE USED depending on the CULTURAL backgrounds of the users. There were DIFFERENT SYSTEMS OF MEASUREMENT. For examples: MASS: kilograms, tonnes, pounds, ounces, grams... LENGTH: inches, feet, millimeters, centimeter, metres, etc. TIME: seconds, minutes, hours, days, etc. TEMPERATURE: Celsius (or Centigrades), Fahrenheits, kelvins This has caused difficulty in COMPARISON and COMMUNICATION (between countries and different disciplines).

What is the relationship between inertial and viscous forces?

Inertial force (in the direction of flow - CAUSE MOTION) and viscous force (in the reverse direction of flow - RESIST MOTION) act in opposite direction. A force that can counterac inertial forces/fluid momemtum is the viscous force/ friction (shear stress).

Define inertial forces

Inertial force, is the force DUE TO THE MOMENTUM OF THE FLUID. This is usually expressed in the momentum equation by the term (ρv)v(ρv)v. So, the denser a fluid and is, and the higher its velocity, the more momentum (inertia) it has. The higher the inertial forces, the higher the momentum of the fluid.

Define isotopes

Isotopes are atoms which have the same atomic number but different mass numbers (due to the presence of different numbers of neutrons in their nuclei)

What is the SI unit for mass?

Kg

Mneumonic for remembering prefixes

Kids Have Droped Dead Converting Metrics Kilo, Hecto, Deca, Deci, Centi, Mili Top, good, models Tera, giga, mega Miss, me, nana Milli, micro, nano

Which type of forces are dominating during the 3 types of fluid flow?

Laminar = viscous forces Transitional = more or less the same Turbulent = inertial forces

What are the values of Rei for laminar flow and turbulent flow in a tank?

Laminar flow = low values of Rei, typically Rei is less than or equal to 10. >> At such low Reynolds numbers liquid moves in regular patterns and will not mix. Turbulent flow = high values of Rei, typically Rei is greater than or equal to 1x10^4. >> The liquid moves in what appears to be a rapid and chaotic manner = mixing occurs.

Discuss laminar fluid flow in a pipe

Laminar flow generally occurs when the fluid is moving slowly or the fluid is very viscous. Ref = 0-2100 Occurs when a fluid flows in parallel layers, with no disruption between the layers. At low velocities, the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards layers of water flowing over one another at different speeds with virtually NO MIXING between layers,

Give examples of when laminar flow occurs

Laminar flow is common only in cases in which the flow channel is relatively small, the fluid is moving slowly, and its viscosity is relatively high. >> Therefor not common in industrial proccesses that often use larger flow channels. Most industrial flows, especially those in nuclear engineering are turbulent. (smoke rising in a straight path from the cigarette).

What are the 3 types of fluid flow in a pipe? And when do they occur IN A PIPE?

Laminar: Ref = 0-2100 Transitional: Ref = 2100-10,000 Turbulent: Ref > 10,000 ^These values (the specific number at which laminar flow occurs) depend ons on the geometry of the flow system and the flow pattern.

How do you do a quick check to see whether an equation is dimensionally homogenous?

Look at the dimensions of the variables in each side of the equations (so T for seconds etc.), and see: 1.) whether they are the same for both sides of the equation 2.) all terms added or subtracted have the same dimensions. 3.) Is the argument inside any trancedental function dimensionless

Give an example demonstrating why it is important to have agreed upon units for substantial variables?

Mars Climate Orbitor: Probe sent by NASA to study waether on Mars - It was destroyed after entering Martian atmosphere > Becuase of units miscommunication Investigation revealed: 1. On board computer used SI units (as per contract agreement) 2. Engineers on Earth used US Imperial units Total cost = 330 M US dollars

Define molar mass. What is its dimensions and what is it also refered to as?

Molar mass is the mass of one mole of substance in g. It is the relative molecular weight (Mr), written in gmol. Mr = mass / moles Has dimensions = MN^-1.

Is the correct term molecular mass or relative molecular mass? Define it

Molecular weight is a measure of the sum of the atomic weight values of the atoms constituting the molecule/compound. It is dimensionless.

Give examples of turbulent fluid flow

Most kinds of fluid flow are turbulent. Key exception = laminar flow at the leading edge of solids moving relative to fluids or extremely close to solid surfaces, such as the inside wall of a pipe, or in cases of fluids of high viscosity (relatively great sluggishness) flowing slowly through small channels. Common examples of turbulent flow are blood flow in arteries, oil transport in pipelines.

Define units

PRECISE PHYSICAL STANDARD against which measurement (of a variable) is made - They are used for measurement of substantial variables/physical quantities

What variables are not included in engineering calculations?

Properties of a body or substance that cannot be quantified by measurements. E.g. taste or aroma, cannot be described completley using appropriate numbers, we can therefore not included these in calculations. >> These are physical QUALITIES not physical QUANTITIES

What is the most important dimensionless variable for pipeline flow? And what is the specific formula for it?

Ref (lowercase f) represents the ratio of INERTIAL FORCES acting on the liquid in the pipe (i.e. those causing motion) to VISCOUS FORCES of the liquid (i.e. those resisting motion) e.g. how fast the fluid is moving (inertial forces) relative to how viscous the fluid is (viscous forces)

Prove that Ref (lower case f) is dimensionless for pipe flow

Ref = (pud) / u = ((MxL^-3)(LT^-1)(L)) / (ML^-1T^-1)) = M^1-1 x L-1+1 x T -1+1 =M^0 x L^0 x T^0 = 1 Therefore no units, and hence a dimensionless variable. Could also prove it, by substituting in the units and cancelling them out.

Discuss transitional fluid flow in a pipe

Ref = 2100 - 10,000 As the Reynolds number increases, such as by increasing the flow rate of the fluid, the flow will transition from laminar to turbulent flow At a specific range of Reynolds numbers, the laminar-turbulent transition range depending on small disturbance levels in the fluid or imperfections in the flow system. On applying external disturbance ,we find there are irregular fluctuations. Intermittent laminar and turbulent flow occur, i.e. phases occur in the flow in which the flow is laminar and phases in which the flow shows turbulent characteristics.

What does the Reynolds number for a stirred tank represent?

Rei (i is lower case) represents the ratio of inertial forces acting on the liquid in a tank (i.e. those causing motion) to viscous forces of the liquid (i.e. those resisting motion). Similar to the Reynolds number for pipe flow.

Is the correct term atomic mass or relative atomic mass? Define it

Relative atomic mass of an element is the weighted mean mass of all the naturally occuring isotopes of an element relative to the mass of an atom of 12C It is relative, as the atomic mass is relative to carbon 12 It is dimensionless (it is just a number/count)

Discuss the mol as a method for expressing the magnitude of a physical variable.

SI base quantity Like a dozen = just a number (substantial variable) Definition: "The amount of substance of a system which contains as many elementary entitites as there are atoms in 0.012 kg (12g) of carbon-12 (isotop of carbon) ". This number is expressed by the Avogadro constant, which has a value of approximately 6.022140857×1023 mol−1 This means that a mole in the SI system is the amount of a substance that contains 6.02x10^23 molecules Denoted by the term grammole or gmol. You can add prefixes to this, e.g. kilogram-mole = 1,000xgmol

Are SI units static?

SI is intended to be an EVOLVING SYSTEM: - prefixes and units are created - unit definitions are modified through international agreement This occurs as the technology of measurement progresses and the precision of measurements improves "The definition and realisation of the base and derived units is an active research topic for metrologists with more precise methods being introduced as they become available".

What is the SI base unit for the base quantity, time? And how was it determined?

Seconds is the base unit of time under the SI system Under the International System of Units (via the International Committee for Weights and Measures, or CIPM), since 1967 the second has been defined as: The duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.

What is the difference between physical quantities and substantial variables?

Substantial variable: a property of a body or substance that can be quantified through measurement (substantial variables have both magnitude and units). Physical quantities: physical property than can be measured (do not need magnitude?) So physical quantities and substantial variables, are the same in that they both quantify/measure a property of a body or substance.

What is the SI base unit for the base quantity, temperature? And how was it determined?

The Kelvin (K) is the base unit of temperature in the IS system. The kelvin is defined as the fraction 1⁄273.16 of the thermodynamic temperature of the triple point of water (exactly 0.01 °C or 32.018 °F).[1] In other words, it is defined such that the triple point of water is exactly 273.16 K. The triple point of water is the unique temperature at which the 3 phases of water (solid, liqud and vapour) co-exist. It is fractionally higher than the melting point of water, being 0.01 degrees celcius or 273.16 K.

In pipeflow what does the Reynolds number tell you? And why is it important?

The Reynolds ( Re ) number is a quantity which engineers use to estimate if a FLUID FLOW IS LAMINAR OR TURBULENT. This is important, because increased mixing and shearing occur in turbulent flow.

What determines the type of fluid flow in a pipe?

The Reynolds number Depending on pipe radius and disturbances in flow the reynolds number changes for the 3 phases.

What are the base quantities and base units of the SI system of measurement?

The SI has recognised 7 quantities as base quantities. The SI has also defined the units of these physical quantities, these are refered to as the base units. "A Measurement System Must Kalculate Kg and Cd"

What is the SI base unit for the base quantity, electricity? And how was it determined?

The ampere (A) is the base unit of electricity in the IS system. The ampere is that constant current which, if maintained in 2 straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacum, would produce between these conductors a force equal to 2x10^7 newton per metre of length.

Define atomic number

The atomic number is equivalent to the number of protons in the nucleus of an atom

What is the SI base unit for the base quantity, light? And how was it determined?

The candela (cd) is the base unit of light in the IS system. The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. The definition describes how to produce a light source that (by definition) emits one candela.

What is the SI base unit for the base quantity, mass? And how was it determined?

The kilogram or kilogramme (SI unit symbol: kg) is the base unit of mass in the International System of Units (SI) Defined as being equal to the mass of the International Prototype of the Kilogram (IPK, also known as "Le Grand K" or "Big K"). It is expected that the definition of the kilogram and several other units will change on May 20, 2019, following a final vote by the CGPM in November 2018.[3] The new definition will use only invariant quantities of nature: the Planck constant, the speed of light, and the caesium hyperfine frequency.[4]

Define mass number

The mass number is the total number of protons and neutrons in the nucleus of an atom

What is the SI base unit for the base quantity, length? And how was it determined?

The metre (is the base unit of length in the SI system The SI unit symbol is m. The metre is defined as the length of the path travelled by light in a vacuum in 1/299 792 458 seconds. The definition has changed many times: 1. originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole 2. In 1799, it was redefined in terms of a prototype metre bar (the actual bar used was changed in 1889) 3. In 1983, the current definition was adopted.

What is the SI base unit for the base quantity, substance? And how was it determined?

The mole (mol) is the base unit of substance in the IS system. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0,012 kilograms of carbon 12.

How was the SI system developed?

The system was published in 1960 as a result of an initiative that began in 1948. It is based on the metre-kilogram-second system of units (MKS). The General Conference of Weights and Measures (GCWM) brought together many international organisations to not only AGREE ON THE DEFINITIONS AND STANDARDS of the new system but also AGRESS ON THE RULES FOR WRITING & PRESENTING MEASUREMENTS IN A STANDARDISED MANNER AROUND THE WORLD.

At what Reynolds numbers does transitional flow occur in a pipe?

The transition from laminar to turbulent flow occurs at a Reynolds number of approximately 2300 in a pipe. However, the precise value depends on: 1. Whether any small disturbances are present. If the experiment is very carefully arranged so that the pipe is very smooth and there are no disturbances to the velocity and so on, higher values of Re can be obtained with the flow still in a laminar state. However, if Re is less than 2300, the flow will be laminar even if it is disturbed. Thus 2300 is the value the Re below which turbulence will not occur in a pipe. 2. If the flow has a different geometry, such as flow in a square duct, or over a turbine blade, transition will occur at different values of Re.

How are were the units of the 7 base quantities decided upon?

The units of a base quantitiy is chosen and aribitraty defined. Think about a dozen. It is chosen to mean 12, and it is chosen randomly.

Define unity bracket

The unity bracket is a method for unit conversion. Consists of a fraction in which the denominator is equal to the numerator (suggested by the "unity" name), but they are in different units. Because the numerator and denominator of the fraction are equal to each other, the fraction is equal to 1. Because of the identity property of multiplication, the value of a number will not change as long as it is multiplied by one. So as long as the numerator and denominator of the fraction are equivalent, they will not affect the value of the measured quantity, but ONLY change the units of the physical variable.

What type of flow is best suited if you want cells and air bubbles to be distributed homogeonusly throughout the tank?

Turbular flow

Discuss turbulent fluid flow in a pipe

Turbulent flow is a type of fluid (gas or liquid) flow in which the fluid undergoes irregular fluctuations, or mixing, in contrast to laminar flow, in which the fluid moves in smooth paths or layers. In turbulent flow the SPEED of the fluid at a point is CONTINOUSLY UNDERGOING CHANGES in both MAGNITUDE and DIRECTION.

You need 1 litre of 25 mM Hepes solution. You have a 1M Hepes stock solution. How much stock solution do you need?

V(stock) x C(stock) = V(final) x C(final) Calculating C(final): 25 mM = 25 x10^-3 M = 0.025 M = 0.025 mol /l V(final) = 1 l C(stock) = 1 M = 1 mol/l V(stock) = (V(final) x C(final)) / C(stock) = (1 l x 0.025 mol/l) / 1 mol/l = 0.025 l = 25 ml

What is the dimension for velocity?

Velocity = L / T Think about the distance=speedxtime triangle.

What is velocity and how is it different from speed?

Velocity is defined as the RATE of travel of an object, along with its DIRECTION It is similar to speed, except that it also adds direction. So, while speed is directionless, velocity is directional speed. Speed only gives you a number that tells you how fast you are going. Velocity, because it adds direction, tells you how fast you are changing your position. Because of this difference, if your position doesn't change even if you are moving very fast, your velocity will be zero

Define viscous forces

Viscous forces are the forces due to to the FRICTION BETWEEN THE LAYERS OF ANY REAL FLUID (viscosity >0) In fluid mechanics we take the fluid as in the continuum condition, which means fluid particles are very closely packed so necessarily there is friction between layers of fluid. The higher the viscous forces, the lower the momentum of the fluid.

How many pounds are in 200 g? Use the unity bracket method. Given 1lb = 453.6 g

Want the grams to cancel out, so in the unity bracket the grams must be in the denominator position.

Do equations without dimensional homogenity exist? If so what are they, what are they called, and when are they used?

When an equation is derived from observation rather than from theoretical principles, it is sometimes convenient to present the equation in a nonhomogenous form (DIMENSIONS OF EITHER SIDE OF THE EQUATION ARE NOT THE SAME) Such equations are called EQUATIONS IN NUMERIES or EMPIRICAL EQUATIONS. In empirical equations, THE UNITS ASSOSCIATED WITH EACH VARIABLE MUST BE STATED EXPLICITYLY.

You have a 100x stock solution of BSA You want to prepare 500 ml of 1x BSA What volume of the stock solution do you have to add?

You dont have to add d(final) here, because it is equal to 1.

What is the SI unit for amount of substance? And is amount always given in this unit?

gmol In the American engineering system, the basic mole unit is the pound-mole or lbmol, which is (6.02x10^23)x453.6 molecules (multiply by 453.6 to get the amoun of molecules in 453.6 g/1 pound). 1 pound = 453.6 g

Give examples of physical variables

length, velocity, viscosity (substantial) also reynolds number (natural)

Give examples of substantial variables

o Mass, weight o Length, area, volume o Time o Temperature o Electric current, voltage, resistance, charge o Number of particles in a matter o Brightness of light o Angle (of reflection, refraction...)

List the 7 most commonly used prefixes

pmol kg Gt mg

What is the equation for calculating volume and concentration of solutions given solutions with volume per volume percent?

volume concentration conc. = (volume of constituent / volume of mixture) x 100 c = (V1/V2) 100 % Used for liquids dissolved in liquids (e.g. detergents