Modern Engineering Thermodynamics

13.2 Part I. Engines and Vapor Power Cycles 455
EXAMPLE 13.2
In 1807, Robert Fulton (1765-1815) successfully piloted his walking beam paddlewheel steamboat Clermont from New York
City to Albany, New York (see Figure 13.5). His single-cylinder engine was made by the Boulton and Watt steam engine
manufacturing company in England and produced 20.0 hp with a piston diameter of 2.00 ft and a piston stroke of 4.00 ft.
The two side paddlewheels were 15.0 ft in diameter. The boiler was made of copper and it weighed 4,000 lbf dry. If the
engine had a duty of 35.0 million and ran at 18.0 strokes per minute, then determine:
a. The average pressure of the cycle.
b. The actual thermal efficiency of the engine.
c. The heat rate produced by the boiler.
Solution
a. The average cylinder pressure of the engine can be determined by setting the calculated power produced by the piston
equal to the actual power produced by the engine, or
_W out = ðp avg Þ × ðPiston displacementÞ × ðPiston strokes/minÞ
" !
#
πðD piston Þ 2
= ðp avg Þ ×
ðPiston strokeÞ × ðStrokes/minÞ
4
πð2:00Þ 2
= ðp avg Þ ×
ft 2 ð4:00 ft/StrokeÞ × ð18:0 Strokes/minÞ
4
= ðp avg Þ × ð226 ft 3 /minÞ
Now,
_W out = 20 hp = (20 hp)(33,000 ft ·lbf/hp·min) = 660,000 ft·lbf/min, so
b. From Eq. (13.1), we have
p avg = 660,000 ft . lbf/min
226 ft 3 /min
η T ð%Þ =
= 2918 lbf/ft 2 2918 lbf/ft2
= = 20:3
144 in 2 lbf/in2
2
/ft
Duty
35:0 × 106
× 100 =
8
8:5 × 10 8:50 × 10 6 = 4:12%
c. The heat rate produced by the boiler can be found from the thermodynamic definition of the thermal efficiency as
η T = _W out = _Q boiler . Then,
_Q boiler =
_ W out
η T
= ð20:0hpÞð2545 Btu/hp . hÞ
0:0412
= 1:24 × 10 6 Btu/h
Exercises
4. Determine the average cycle pressure in Example 13.2 if the engine produces 30.0 instead of 20.0 hp and all the other
variables remain unchanged. Answer: p avg = 27.3 psi.
5. Determine the actual thermal efficiency of the engine in Example 13.2 if it has a duty of 26.0 × 10 6 instead of
35.0 × 10 6 and all the other variables remain unchanged. Answer: η T = 3.06%.
6. Determine the heat rate produced by the boiler in Example 13.2 if the engine produces 25.0 instead of 20.0 hp, and all
the other variables remain unchanged. Answer: _Q boiler = 1.55 × 10 6 Btu/h.
WHAT IS A STEAM ENGINE INDICATOR?
In an effort to continue to improve the performance of his steam engines, Watt wanted to know how the pressure varied
with piston position inside the cylinder as the engine was running. About 1790, he developed an ingenious device for this
purpose (Figure 13.6), which he called a steam engine indicator. This device drew the actual pressure–volume diagram of the
steam inside the cylinder as the engine was running. Such p V diagrams soon became known as indicator diagrams, and the
area enclosed by these diagrams represented the reversible work produced inside the engine.
(Continued)