Question 13.1: In 1765, John Smeaton built a small steam engine with a 10.0...
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.
The work required by Smeaton’s engine to raise 291,900 \text{lbf } of water 10.0 \text{ft } in height was mg(Δh) = 2,919,000 \text{ft · lbf.} Therefore, it could have raised 2,919,000 \text{lbf} of water 1 \text{ft } in height using the same amount of work. Since the duty of any engine is the amount of water it can raise 1 \text{ft } when one 84.0 \text{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
η_T(\text{in})\% = \frac{\text{Duty}}{8.50 × 10^8} × 100 (13.1)
η_T = \frac{\text{Duty}}{8.5 × 10^8} × 100 = \frac{2,919,000}{8.5 × 10^8} × 100 = 0.344\%
His engine was not very efficient.