Modern Engineering Thermodynamics

28 CHAPTER 1: The Beginning
6. Most people believe that the size of a shoe is the length of the shoe
in inches (Figure 1.25). Curiously, this is not the case. Shoe sizes
became standardized between 1850 and 1900 as factory-made
shoes became popular. The size standardization consisted of
defining the smallest shoe size at some fixed insole length, then
increasing the insole length by a fixed amount for each size
increment. The child’s size 0 shoe was specified to have a 3 11
12 inch
long insole and the adult size 1 shoe (there is no size 0 adult shoe)
was specified to have an 8 7 12
inch long insole. It was also decided
that each full size increment would represent an increase in insole
length by one barleycorn ( 1 3
inch), and an increase in girth
(the internal circumference of the shoe and the ball of the foot)
by 1 4
inch. Letters were chosen to denote shoe width increments,
and the difference in girth between these width increments
(for example, between a C and a D width shoe) is also 1 4 inch.
a. Determine the equations that relate the adult and child’s size
directly to insole length, and compute the insole length of
an adult size 10 shoe.
b. Compute the size of a child’s shoe that has the same insole
length as a size 1 adult shoe and explain why children’s
shoes are not available in size 14 or larger.
8d Common
8d Common brad
8d Flooring brad
8d Casing
8d Finishing
6d Shingle nail
8d Clinch nail
3d Fine nail
3d Slating nail
1 inch Barbed roofing nail
FIGURE 1.26
Problem 7.
FIGURE 1.25
Problem 6.
One foot!
7. The classification of carpenters’ nails is based on a unit system
that is at least six centuries old. The penny system of nail sizing,
usually designated by d, the letter that was also the symbol for
the monetary penny or pence (i.e., 3d = 3 penny nail),
originated in medieval England. 9 At that time, nails were sold
by the hundred, and originally a hundred 3 penny nails cost 3
pennies. From this practice came the classification of nail sizes
according to the price per hundred (Figure 1.26). This system
had the disadvantage that inflation in the monetary system
caused the size of the nails to change. By the end of the 15th
century, the classification became standardized according to
Table 1.9 10 ; and from this point on, the size of the nails no
longer corresponded to their actual cost. Estimate the percent of
monetary inflation since the 15th century if a pound of 6d nails
currently costs $1.00.
8. By 1724, Gabriel Daniel Fahrenheit (1686–1736) had
established his well-known temperature scale. This scale was based
on two fixed points: the freezing point of a water and ammonium
chloride solution (called 0°F) and the temperature of the human
body (called 96°F). Later adjustments to the scale shifted the body
temperature to 98.6 EF. What advantages did the number 96 have
over, say, 100 as an upper end to this scale in 1724?
9. Determine the units of thermal conductivity, k t , as defined by
the following equation: _Q = –k t A(dT/dx), where _Q is the heat
transfer rate in watts, A is the cross-sectional area in m 2 , T is the
absolute temperature in K, and x is the distance in m.
10. Determine the units of viscosity, μ, in the following equation:
τ = μ(du/dy), where τ is a shear stress, u avelocity,andy is a distance
in (a) the Engineering English system, and (b) the SI system.
11. Develop a unit conversion factor to convert the specific heat of a
substance in calories/(g·K) into Btu/(lbm·R).
12. The specific internal energy of a system is 411.7 J/kg. Express
this value in the following units: (a) ft·lbf/lbm, (b) kcal/kg, and
(c) kW·h/lbm.
13. Determine the weight at standard gravity of 10.0 lbm in (a) lbf,
(b) poundals, (c) dynes, and (d) newtons.
Table 1.9 Nail Sizes
Nail Size
2d 3d 4d 5d 6d 7d 8d 9d 10d 12d 16d 20d 30d 40d 50d 60d
Length (inches) 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 4.00 4.50 5.00 5.50 6.00
Number per pound 845 540 290 250 165 150 100 90 65 60 45 30 20 17 13 10
9 The d is from denarius, the name of an old Roman silver coin.
10 Nails less than 2 penny in size are called tacks or brads, and nails larger than 60 penny are called spikes.