Modern Engineering Thermodynamics

452 CHAPTER 13: Vapor and Gas Power Cycles
By the late 1760s, John Smeaton (1724–1792) 3 had undertaken a study of the fuel efficiencies of a number of
England’s Newcomen steam engines. He called his measure of fuel efficiency the duty of the engine, and he
defined it as follows:
The duty of a pumping engine is equal to the number of pounds of water that are raised one foot in height
by the engine’s pump when one 84.0 lbm bushel of coal is burned in the boiler.
Because Smeaton’s efficiency (duty) was applied to the total energy conversion process from chemical input
(coal) to work output (water pumped), it constituted a measure of the overall system efficiency that included
the boiler and pump efficiencies and the efficiency of the piston-cylinder operation. Byassumingtheaverage
energy content of coal to be 1.30 × 10 3 Btu/lbm, we can easily convert Smeaton’s duty measurements into overall
thermal efficiencies. One 84.0 lbm bushel (bu) of coal = (1.30 × 10 3 Btu/lbm)(84.0 lbm/bu)(778.16 ft · lbf/
Btu) = 8.50 × 10 8 ft· lbf of energy. Defining thermal efficiency η T as the ratio of net output (pounds of water
raised 1 ft) to net input (ft·lbf of energy of coal consumed), we obtain (in percent)
η T ðin%Þ =
Duty
× 100 (13.1)
8
8:50 × 10
EXAMPLE 13.1
In 1765, John Smeaton built a small steam engine with a 10.0 in (0.254 m) diameter piston having a 38.0 in (0.965 m)
stroke and found that, when it was used to drive a water pump, it could pump 291,900 lbf of water 10.0 ft high when one
84.0 lbm bushel of coal was burned in the boiler. Determine the duty and thermal efficiency of this engine.
Solution
The work required by Smeaton’s engine to raise 291,900 lbf of water 10.0 ft in height was mg(Δh) = 2,919,000 ft · lbf.
Therefore, it could have raised 2,919,000 lbf of water 1 ft in height using the same amount of work. Since the duty of
any engine is the amount of water it can raise 1 ft when one 84.0 lbm bushel of coal is burned in the boiler, the duty of
Smeaton’s engine is 2,919,000. Note that, because of the way duty is defined, it is expressed without units or dimensions.
Then, Eq. (13.1) gives the thermal efficiency of Smeaton’s engine as
His engine was not very efficient.
η T =
Duty
2,919,000
× 100 = × 100 = 0:344%
8 8
8:5 × 10 8:5 × 10
Exercises
1. Suppose Smeaton’s engine in Example 13.1 had pumped 291,900 lbf of water 15.0 ft high. What would its duty and
thermal efficiency be in this case? Answer: Duty = 4,378,500 and η T = 0.515%.
2. How high would Smeaton’s engine in Example 13.1 have to pump 1.00 lbf of water to have a duty of 5,000,000?
Answer: Δh = 5,000,000 ft.
3. What would be the duty of Smeaton’s engine in Example 13.1 if it had a thermal efficiency of 10%?
Answer: Duty = 85.0 × 10 6 .
For five years, Smeaton collected duty measurements for over 30 Newcomen pumping engines and found they
had an average duty of 5,590,000, which corresponds to an average overall thermal efficiency of 0.65%. With
these results he was able to conclude that large diameter pistons with short strokes made the most efficient
engines. Using this result and improved cylinder boring techniques (necessary to reduce piston leakage), he was
able to build an engine with a 52.0 in (1.32 m) diameter piston and a 7.00 ft (2.13 m) stroke in 1772 that had
a duty of 9,450,000 and an overall thermal efficiency of 1.11%. Thus, he was able to produce an engine with
double the efficiency of the average Newcomen engine simply by using his experimental observations to optimize
its design.
3 John Smeaton was a successful English engineer. In about 1750, he introduced the name civil engineer for any nonmilitary engineer
(civil being simply a contraction of the word civilian). In 1771, he started the British Institution of Civil Engineers (the world’s first
professional engineering society). This was followed by the founding of the British Institution of Mechanical Engineers in 1847 by
George Stephenson (1781–1848). In America, the American Society of Civil Engineers (ASCE) was founded in 1852. This was followed
by the American Institute of Mining Engineers (AIME) in 1871, the American Society of Mechanical Engineers (ASME) in 1880, the
American Institute of Electrical Engineers (AIEE) in 1884, the Society of Automotive Engineers (SAE) in 1904, American Institute of
Chemical Engineers (AIChE) in 1908, and many others.