To determine Find the work done to pump the kerosene to level of the top of the tank. Explanation Given information: The height of the vertical right–circular cylindrical tank is 30 ft. The diameter of the vertical right–circular cylindrical tank ( d ) is 20 ft. The unit weight of kerosene ( γ ) is 51.2 lb/ft 3 . Calculation: The typical slab volume between the planes at y and y + Δ y is Δ V . Determine the typical slab volume using the relation. Δ V = π r 2 Δ y = π × ( d 2 ) 2 Δ y Here, Δ y is the thickness. Substitute 20 ft for d . Δ V = π ( 20 2 ) 2 Δ y = ( 100 π Δ y ) ft 3 The force required for lifting slab is equal to the weight of the slab. Determine the required force using the relation. F = γ × Δ V Substitute 51.2 lb/ft 3 for γ and ( 100 π Δ y ) ft 3 for V . F = 51.2 × 100 π Δ y = ( 5 , 120 π Δ y ) lb Determine the work taken to lift the kerosene using the relation. Δ W = F × h Here, h is the distance through which F must act. Substitute ( 5 , 120 π Δ y ) lb for F and ( 30 − y ) ft for h . Δ W = ( 5 , 120 π Δ y ) ( 30 − y ) = [ 5 , 120 π ( 30 − y ) Δ y ] ft-lb Determine the approximate work taken to pump the entire kerosene using Riemann sum

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Chapter 6.5, Problem 19E

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Find the work done to pump the kerosene to level of the top of the tank.

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Chapter 6.5, Problem 18E

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