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6.6 Notes (Work Part 2)

# 6.6 Notes (Work Part 2) - liquid being pumped out 7 Set up...

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Work Continued (Section 6.6) Pumping Problems Example 0.1. An aquarium with dimension 3 0 × 1 0 × 2 0 is full of water. Find the work required to pump all the water over the top of the tank. 1. Draw tank and add a coordinate system. 2. Draw a thin slice of water with height Δ x and find the volume Δ V of the slice. 3. Find the weight (force) F of the slice. For water, the weight is 62.5 lb/ft 3 or 9800 kg/m 3 . 4. Find the distance the slice must travel to get out. 5. Find the work Δ W to lift the slice. Δ W = Fd . 6. Determine the limits of integration. They will be determined by the amount of

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Unformatted text preview: liquid being pumped out. 7. Set up integral W = Z b a Δ W and evaluate. Example 0.2. Find the work done to pump water over the rim of a trough which is 10 ft long and has a semicircular end with a diameter of 6 ft if the tank is 2/3 full of water. Example 0.3. A tank in the form of a right circular cone, vertex down, is ﬁled with water. If the height is 10 ft and its diameter is 4 ft, ﬁnd the work done to pump all the water out of an opening 2 ft above the tank....
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