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.
- 0 variables
- 2 worked examples
- 14 in Applications of Integrals
Worked examples
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
1 more worked examplePremium
A rectangular tank with a 2 m × 3 m base and depth 4 m is full of water. Find the work to pump it all out over the top edge.
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Practice
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