Applications of Integrals · Work & Force
Work (Pumping)
Work to pump fluid out of a tank. A(y) is the cross-sectional area at height y, h is the height to which fluid is pumped.
- 2 worked examples
- 14 in Applications of Integrals
Worked examples
- A(y) = π(2²) = 4π. Pump to height h = 5.
- W = ∫₀⁵ 1000(9.8)(4π)(5-y) dy = 39200π ∫₀⁵ (5-y) dy
- = 39200π[5y - y²/2]₀⁵ = 39200π(25-12.5) = 39200π(12.5)
Answer: 490,000π ≈ 1,539,380 J
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Common questions
What is the Work (Pumping)?
Work to pump fluid out of a tank. A(y) is the cross-sectional area at height y, h is the height to which fluid is pumped. It is one of the applications of integrals formulas in the CalcRef reference.
How do you use the Work (Pumping)?
Worked example. Find the work to pump water out of a full cylindrical tank of radius 2m and height 5m. A(y) = π(2²) = 4π. Pump to height h = 5. W = ∫₀⁵ 1000(9.8)(4π)(5-y) dy = 39200π ∫₀⁵ (5-y) dy. = 39200π[5y - y²/2]₀⁵ = 39200π(25-12.5) = 39200π(12.5). Answer: 490,000π ≈ 1,539,380 J.
Practice
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