Time, metric units

Between 1869 and the beginning of World War I, most of the world s supply of potassium salts came from the Stassfurt deposits in Germany. During World War I, U.S. production, measured as K2O, rose from 1000 metric tons in 1914 to 41,500 t in 1919. Following the end of World War I, U.S. production declined as imports increased. By the time the United States entered World War II, however, production had expanded enough to meet domestic needs. Since then, production has fluctuated, but has fallen below consumption as of the mid-1990s. Total annual U.S. demand peaked at 6.9 X 10 t in 1979 and has leveled off at approximately 5.1 to 5.5 million t. Canada is the principal potash exporter. 

We thus see that acceleration is a vector and describes how velocity changes with time. Let s take a more careful look at the units on acceleration. In the official metric units, velocity has units of m/s. Acceleration is velocity divided by time, with units of seconds. If we divide m/s by s, we get m/s2. These are the units for acceleration, but you might find it useful to think of them in terms of meters per second per second. That is, how velocity (m/s) changes with each second of time. 

C = coefficient of heat conductivity measured in heat units per unit time per unit of packing volume per deg temperature difference usual units are cal per sec per deg C per cc m = a constant for limestone packings, m = 0.0073 for iron ore, 0.0105 anthracite and other coals, 0.0050 blast-furnace charge, 0.0072. The values are in metric units. q = volume of gas flow per unit-time per square unit of cross-sectional packing area, expressed as liters per sec per sq cm T = temperature, deg abs, C = fractional voids (dimensionless) d = diameter of particles, cm... 

Dimensionless analysis — Use of dimensionless parameters (-> dimensionless parameters) to characterize the behavior of a system (- Buckinghams n-theorem and dimensional analysis). For example, the chronoampero-metric experiment (-> chronoamperometry) with semiinfinite linear geometry relates flux at x = 0 (fx=o, units moles cm-2 s-1), time (t, units s-1), diffusion coefficient (D, units cm2 s-1), and concentration at x = oo (coo, units moles cm-3). Only one dimensionless parameter can be created from these variables (-> Buckingham s n-theorem and dimensional analysis) and that is fx=o (t/D)1/2/c0C thereby predicting that fx=ot1 2 will be a constant proportional to D1/,2c0O) a conclusion reached without any additional mathematical analysis. Determining that the numerical value of fx=o (f/D) 2/coo is 1/7T1/2 or the concentration profile as a function of x and t does require mathematical analysis [i]. 

The relationship between shearing stress and rate of shear can be used to define the flow properties of materials. In the simplest case, the shearing stress is directly proportional to the mean rate of shear x = fly (Figure 8-5). The proportionality constant T is called the viscosity coefficient, or dynamic viscosity, or simply the viscosity of the liquid. The metric unit of viscosity is the dyne.s cm-2, or Poise (P). The commonly used unit is 100 times smaller and called centiPoise (cP). In the SI system, t is expressed in N.s/m2. or... 

The third column of Table 1 shows the metric units that may be used for an indefinite period of time witii SI. These include the minute, hour, year, and liter. The fourth column contains units tiiat are accepted for a limited period of time, probably on the order of five to 10 years, aldiough this duration has not been established by the Institute. And finally, the fifth column lists diose units that are definitely outside SI. and which will not be allowed in AIChE publications. 

The standards behind the English units are not reproducible. Arms, hands, and grains of barley will obviously vary in size the size of a 3-foot yard depends on whose feet are in question. But metric units are based on standards that are precisely reproducible, time after time. 

Traditionally, measurements in the clinical laboratory have been made in metric units. In the early development of the metric system, units were referenced to length, mass, and time. The first absolute systems were based on the centimeter, gram, and second (CGS) and then the meter, kilogram, and second (MKS). The SI is a different system that was accepted internationally in 1960. The units of the system are called SI units. 

Metric system. The system of units used by scientists in which multiples or subdivisions of units are powers of 10 times the unit, and all such multiples or subdivisions are designated by the same prefix no matter what unit is involved. 

The standard metric unit of time is the second. The need for accurate measurement of time by chemists may not be as apparent as that associated with mass, length, and volume. It is necessary, however, in many applications. In fact, matter may be characterized by measuring the time required for a certain process to occur. The rate of a chemical reaction is a measure of change as a function of time. 

The standard metric unit of length is the meter. Large distances are measured in kilometers smaller distances are measured in millimeters or centimeters. Very small distances (on the atomic scale) are measured in nanometers (run). The standard metric unit of volume is the liter. A liter is the volume occupied by 1000 grams of water at 4 degrees Celsius. The standard metric unit of time is the second, a unit that is used in the English system as well. 

To do this we will load a helpful package called Miscellaneous Units from Mathematica. We also want graphs of the predicted catalyst mass as function of time, the theoretical level of catalytst in the reactor as a function of time, and the actual level that has been measured in the reactor at a few times during the loading process. Finally, we can compute the catalyst cost in flowing into the reactor volume per unit time. Here we calculate the mass flow in per unit time in metric units as well as the volume and cross-sectional area of the reactor. 

In chemical engineering practice, we tend not to use the very large or small ends of the table, but you should know at least as large as mega (M), and as small as nano (n). The relationship between different sizes of metric units was deliberately made simple because you will have to do it all of the time. You may feel uncomfortable with it at first if you re from the U.S. but trust me, after working with the English system you ll learn to appreciate the simplicity of the Metric system. 

The second advantage of the modern metric system is that standards for most fundamental units are defined by reproducible phenomena of nature. For example, the metric unit for time—the second— is now defined in terms of a specific number of cycles of radiation from a radioactive cesium atom, a time period beheved never to vary. 

Common prefixes for metric units—which may apply in more cases than shown below—include giga- (1 billion times the unit), mega- (one million times), kih- (1,000 times), hecto- (100 times), deka- (10 times), deci- (0.1 times, or one tenth), centi-(0.01, or one hundredth), milli- (0.001, or one thousandth), and micro- (0.0001, or one millionth). 

Section 1.4 Measurements in chemistry are made using the metric system. Special emphasis is placed on a particular set of metric units called SI units, which are based on the meter, the kilogram, and the second as the basic units of length, mass, and time, respectively. The metric system employs a set of prefixes to indicate decimal fractions or multiples of the base units. The SI temperature scale is the Kelvin scale, although the Celsius scale is frequently used as well. Density is an important property that equals mass divided by voliune. 

Since the United States is the only major industrial nation that has not yet converted to metric units, some legal requirements in that direction are to be expected. It is now a contradiction to speak of the English system of units, and for some time to come U.S. engineers must accommodate to a wide use of conversions from one set of units to another. The extensive conversion tables that follow are offered with this expectation. 

The decision over which units to use is societal. Americans have consistently differed from the rest of the world in using English units over metric units. We are slowly changing, however, and with time, we should be consistent with other nations. For scientific measurements, always use metric units (2.4). 

In 1960 the General Conference of Weights and Measures adopted the International System of units (or SI, after the French le Systeme International d Unites), which is a particular choice of metric units. This system has seven SI base units, the SI units from which all others can be derived. Table 1.2 lists these base units and the symbols used to represent them. In this chapter, we will discuss four base quantities length, mass, time, and temperature. ... 

Larger and smaller metric units are identified by metric symbols, or prefixes. The prefix for the unit 1000 times larger than the base unit is kilo-, and its symbol is k. 

The metric unit is the NEWTON, N, whose dimensions are kg m/sec. A newton is thus the force needed to change the velocity of a mass of 1 kg by 1 m/second in a time of 1 second. However, the older unit, the DYNE (defined below) is still very much in use. 

The SI and metric unit of time is the second (s). However, we also measure time in units such as years (y), days, hours (h), or minutes (min). The standard device now used to determine a second is an atomic clock. Some useful relationships between different units for time follow ... 

In the examples given in the preceding section, both British and metric units were used. For example, the mile is a British unit of distance, while the meter is a metric unit kilogram is metric units of time, e.g., the second, are both British and metric. Science, however, tends almost exclusively to use the metric system, and that will be the general practice in this book. 

The Joule is equal to a 1 N m, but is reserved for a unit of energy and can have more than one application, as discussed later. When we get into thermal stresses and heat transfer, it is confusing to nse Jonle as a bending moment of torque and as a thermal unit. We will spend more time later on the proper use of metric units. 

---