English engineering system

Equation (1.3) is an expression for the work done as a result of a finite compression or expansion process, t This kind of work can be represented as an area on a pressure-vs.-volume (PV) diagram, such as is shown in Fig. 1.3. In this case a gas having an initial volume Vt at pressure Pi is compressed to volume V2 at pressure P2 along the path shown from 1 to 2. This path relates the pressure at any point during the process to the volume. The work required for the process is given by Eq. (1.3) and is represented on Fig. 1.3 by the area under the curve. The SI unit of work is the newton-meter or joule, symbol J. In the English engineering system the unit often used is the foot-pound force (ft lbr). 

Other systems of units, such as the English engineering system, use units thai are related to SI units by fixed conversion factors. Thus, the foot (ft) is defined as 0.3048 m, the pound mass (lbm) as 0.45359237 kg, and the pound mole (lb mof as 453.59237 mol. 

In the English engineering system of units, force is treated as an additions independent dimension along with length, time, and mass. The pound force (lbr is defined as that force which accelerates 1 pound mass 32.1740 feet per seconc per second. Newton s law must here include a dimensional proportionality constant if it is to be reconciled with this definition. Thus, we write... 

The pressure P of a fluid on a surface is defined as the normal force exerted by the fluid per unit area of the surface. If force is measured in N and area in m2, the unit is the newton per square meter or N nTJ, called the pascal, symbol Pa, the basic SI unit of pressure. In the English engineering system the most common unit is the pound force per square inch (psi). 

In the English engineering system, kinetic energy is expressed as mu2/gc, where gc has the value 32.1740 and the units (lbm)(ft)(lbf) l(s) 2. Thus the unit of kinetic energy in this system is... 

In the English engineering system, potential energy is expressed as mzgfge. Thus the unit of potential energy in this system is... 

The units of all terms of this equation must be the same. The product PV has the units of energy, as does U therefore H also has units of energy. In the SI system the basic unit of pressure is the pascal or N m"2 and, for volume, the m3. Thus the PV product has the unit N m or joule. In the English engineering system a common unit for the PV product is the (ft lbr), which arises when pressure is in (lbr)(ft) 2 with volume in (ft)3. This result is usually converted to (Btu) through division by 778.16 for use in Eq. (2.6), because the common English engineering unit for U and H is the (Btu). 

This equation is the mathematical expression of the first law for a steady-state-flow process. All the terms are expressions for energy per unit mass of fluid in the SI system of units, energy is expressed in joules or in some multiple of the joule. For the English engineering system of units, this equation must be reexpressed to include the dimensional constant gc in the kinetic- and potential-energy terms ... 

It is recognized at this time that the English Engineering System of units cannot be completely replaced by the International System (SI). Transition from the English system of units to SI will proceed at a rational pace to accommodate the needs of the profession, industry, and the public. The transition period will be long and complex, and duality of units probably will... 

Equation 4Ab can be used only if we can find a way to assign numerical values to the various symbols in it. We already have an expression for work, Eq. 4.1. It has the dimension of force times distance in SI its unit is the joule (lJ = N-m). In the English engineering system-of units, its unit is the foot-pound force, abbreviated ft lbf. 

Most students, at various levels, are probably familiar with unit systems. In this chapter we will provide some details on the International System of Units and its relation to the English Engineering system. Our main purpose is to ensure that students cannot only use the different systems but also convert units among different systems. In addition, students will gain an understanding of the different approximate dimensions and sizes that occur frequently in the field of chemical and bioprocess engineering. 

Table 2.2 Derived units and parallels between English Engineering system units and SI units ...

The above table (Table 2.2) was constructed considering the most relevant derived units at this stage of your engineering studies and depicting the parallels between SI and English Engineering system units. It is not exhaustive but will be very useful for all situations and problems presented in this book. 

The following table (Table 2.3) presents some equivalences between the SI and English Engineering system units. 

In the SI system, where length, mass, and time are defined as primary dimensions and force a secondary dimension, is equal to 1. In the English Engineering system mass and force are defined... 

Table 2.3 Unit measurements in SI and English Engineering system and its corresponding equivalences ...

In the English Engineering system, should always be used when mass and force are related. It is normally present in calculations of, for example, work and power. 

Process variables are chemical and physical properties involved in the streams of different processes of a complete system. The most common process variables at this stage of your development are mass, volume, density, moles, pressure, and temperature and will be discussed in some detail in terms of the main units and conversions between SI and English Engineering systems. 

In the SI system, mass is measured in kilograms (kg) and in the English Engineering system in pounds (lb). As presented in Table 2.3, the equivalence between these systems is... 

Note that the Reynolds number is a DN. In addition, you can check and obtain the same result working with the English Engineering system. 

The Old English Engineering system of units uses pound (lb) for force, pound (lb) for mass, foot (ft) for length, and second or hour (s or hr) for time. Note that lb for force and lb for mass are not stipulated in this system of units. You have to be an astute, careful reader to distinguish which pound an author is using. This system of units has caused much confusion among scientists and engineers. 

In other words, we have two independent variables and one dependent variable. We can specify the dimensions for any two variables, thereby allowing the third variable to become the dependent variable whose dimensions are derived from the dimensions of the other two variables. However, when we specify the dimensions of all three variables, we overspecify the equation. Thus in the Old English Engineering system of units Newton s second law has units of... 

What about go In the Old English Engineering system of units we... 

The dimensional constant = 32.2 ft lb /lby s is included here because these equations are still sometimes used with the English engineering system of units in SI units. 

N m = J = V C = W s = several other combinations. In the English engineering system there is no comparable simplification. 

We can easily show the equivalent of this for rotating shafts or electrical or magnetic work. In the English engineering system the unit of work is the ft Ibf, and in SI the N m = J. In the SI system the electrical units were chosen so that... 

The dimensional constant = 32.2 ft-lb /lbf-s is included here because these equations are still sometimes used with the English engineering system of units.) Since = (i /2)(dP/dx) (the minus sign has been dropped, it being understood that flow is in the direction of decreasing pressure), then... 

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