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Math practice questions

28 questions from the boiler operator and stationary engineer practice test.

Math practice test

10 questions, graded as you go, with the reason for every answer. No sign-up.

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Sample questions

A boiler is rated at 150 boiler horsepower. What is its rated heat output in Btu per hour? (1 BHP = 33,475 Btu/hr)

Answer in Btu/hr.

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5021250 Btu/hr

Output = BHP × 33,475 = 150 × 33,475 = 5,021,250 Btu/hr.

Reference: Boiler horsepower: 33,475 Btu/hr

How many Btu are needed to heat 500 gallons of water from 60°F to 180°F? Use 8.34 lb per gallon and a specific heat of 1 Btu/lb·°F.

Answer in Btu.

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500400 Btu

Weight = 500 gal × 8.34 lb/gal = 4,170 lb. Temperature rise = 180 − 60 = 120°F. Heat = 4,170 lb × 1 Btu/lb·°F × 120°F = 500,400 Btu.

Reference: Sensible heat: Q = W × c × ΔT; water 8.34 lb/gal

A safety valve disc is exposed to boiler pressure over a circular area 3 in. in diameter. What is the total upward force on the disc at 100 psi? Use area = 0.7854 × D².

Answer in lb.

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706.9 lb

Area = 0.7854 × 3² = 0.7854 × 9 = 7.069 in². Force = pressure × area = 100 psi × 7.069 in² = 706.9 lb.

Reference: Force = pressure × area

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