Explanation Given information: The height of the well ( H ) is 300 ft. The diameter of the pipe ( d ) is 4 in.. The diameter of the cylindrical tank ( D ) is 20 ft. The height of the cylindrical tank ( h ) is 25 ft. The location of the tank from the ground is 60 ft. The power of the pump ( P ) is 3 hp with the rating of 1 , 650 ft ⋅ lb sec . The unit weight of water ( γ ) is 62.4 lb/ft 3 . Calculation: Consider the typical slab between the planes at y and y + Δ y has a volume of Δ V . Determine the volume of the tank using the relation. Δ V = π D 2 4 × t Substitute 20 ft for D and Δ y for t . Δ V = π × 20 2 4 × Δ y = ( 100 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 62.4 lb/ft 3 for γ and ( 100 π Δ y ) ft 3 for Δ V . F = 62.4 × ( 100 π Δ y ) = 6 , 240 π Δ y lb Determine the work done to lift the slab using the relation. Δ W 1 = Force × distance The distance through which F must act is y ft. Substitute 6 , 240 π Δ y lb for Force and y ft for distance. Δ W 1 = 6 , 240 π Δ y × y ft-lb Take the limit for the integral from above the water surface to base of the tank and the top of the tank. Write the Riemann sum for the work taken to lift all the water into the tank. W 1 ≈ ∑ 360 385 Δ W 1 Substitute 6 , 240 π Δ y × y ft-lb for Δ W 1 . W 1 ≈ ∑ 360 385 6 , 240 π Δ y × y ft-lb Determine the work taken to lift all the water into the tank using the relation. W 1 = ∫ 360 385 Δ W 1 d y Substitute 6 , 240 π Δ y × y ft-lb for Δ W 1 . W 1 = ∫ 360 385 6 , 240 π y d y = 6 , 240 π [ y 2 2 ] 360 385 = 6 , 240 π [ ( 385 2 2 − 360 2 2 ) ] = 182 , 557 , 949 ft-lb Pipe filling: Determine the volume of the tank using the relation. Δ V = π d 2 4 × t Substitute 4 in. for d and Δ y for t . Δ V = π × ( 4 in . × 1 ft 12 in . ) 2 4 × Δ y = ( π 36 Δ y ) ft 3 Determine the force using the relation

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ISBN: 9780136208105

Author: Hass

Publisher: PEARSON

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Chapter 6.5, Problem 32E

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Find the time taken to fill the tank first time to the nearest hour.

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Chapter 6.5, Problem 31E

Chapter 6.5, Problem 33E

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UNIV CALCULUS EARLY TRANS (LL) W/MYLAB

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