Explanation Given information: The height of the right circular cylindrical tank ( h ) is 10 ft. The radius of the right circular cylindrical tank ( r ) is 5 ft. The unit weight of diesel fuel ( γ ) is 53 lb/ft 3 . The point where the fuel to pump is 15 ft above the top of the tank. Calculation: Consider the typical slab between the planes at y and y + Δ y has the volume as Δ V . Determine the volume of the tank using the relation. Δ V = A × t = π r 2 × t Here, A is the area of the slab and t is the thickness of the slab. Substitute 5 ft for r and Δ y for t . Δ V = ( π ( 5 ) 2 Δ y ) = ( 25 π Δ y ) ft 3 The force needed to lift the slab is equal to the weight of the slab. Determine the force F using the relation. F = γ × Δ V Substitute 53 lb/ft 3 for γ and ( 25 π Δ y ) ft 3 for Δ V . F = 53 × ( 25 π Δ y ) = 1 , 325 π Δ y lb Determine the work done to lift the slab using the relation. Δ W = Force × pumping distance The fuel need to be pumped at the distance of 15 ft above the top of the tank. Therefore, the pumping distance is taken as ( 25 − y ) ft . Substitute 1 , 325 π Δ y lb for Force and ( 25 − y ) ft for pumping distance. Δ W = 1 , 325 π Δ y ( 25 − y ) ft-lb Write the Riemann sum for the approximate work done to lift the entire slab

Thomas' Calculus: Early Transcendentals in SI Units

14th Edition

ISBN: 9781292253114

Author: Hass, Joel R., Heil, Christopher E., WEIR, Maurice D.

Publisher: PEARSON

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Chapter 6.5, Problem 22E

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Find the work needed to pump the entire fuel to a point 15 ft above the top of the tank.

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Chapter 6.5, Problem 21E

Chapter 6.5, Problem 23E

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