Explanation Given: The tank is half filled with oil. The radius r of the tank is 3 m. Take the weight density of the oil w o i l as 900 kg/m 3 . Show the expression to find the work done W to pump the oil from a to b . W = lim n → ∞ ∑ i = 1 n f ( x i ∗ ) Δ x = ∫ a b f ( x ) d x (1) Calculation: Consider the value of acceleration due to gravity g as 9.8 m/s 2 Show the section of water tank as in Figure 1. Refer to Figure 1. The oil extends from 0 m to 3 m. Divide the interval [ 0 , 3 ] into n sub intervals with endpoints y 0 , y 1 , ... , y n . Choose y i ∗ in the i t h subinterval. The i t h layer is a cylindrical slice with radius r i and depth Δ y . Calculate the radius of the cylindrical slice using the relation: O B 2 = A B 2 + O A 2 3 2 = r i 2 + ( y i ∗ ) 2 r i = 9 − ( y i ∗ ) 2 Calculate the volume of the cylindrical slice at i t h subinterval as shown below: V = π r i 2 h (2) Substitute 9 − ( y i ∗ ) 2 for r i and Δ y for h in Equation (2). V = π 9 − ( y i ∗ ) 2 2 Δ y = ( 9 − ( y i ∗ ) 2 ) π Δ y m 3 Calculate the weight of the oil w in the rectangular slice. w = w o i l × V = ρ o i l g × V (3) Here, ρ o i l is the mass density of the oil and V is the volume. Substitute ( 9 − ( y i ∗ ) 2 ) π Δ y m 3 for V and 900 kg/m 3 for ρ o i l in Equation (3). w = 900 × 9.8 × ( 9 − ( y i ∗ ) 2 ) π Δ y N = 8820 × ( 9 − ( y i ∗ ) 2 ) π Δ y N Calculate the work done W i to pump the oil from the rectangular slice using the relation. W i = F × d (4) Here, F is force and d is distance

Bundle: Single Variable Calculus: Early Transcendentals, Loose-leaf Version, 8th + Webassign Printed Access Card For Calculus, Multi-term Courses, Life Of Edition

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ISBN: 9780357008034

Author: Stewart

Publisher: CENGAGE L

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Chapter 6.4, Problem 28E

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To calculate: The work done to pump out the oil from the tank through the spout.

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Chapter 6.4, Problem 27E

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Bundle: Single Variable Calculus: Early Transcendentals, Loose-leaf Version, 8th + Webassign Printed Access Card For Calculus, Multi-term Courses, Life Of Edition

Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Find the area of the shaded region.Ch. 6.1 - Sketch the region enclosed by the given curves....Ch. 6.1 - Sketch the region enclosed by the given curves....Ch. 6.1 - Prob. 7E Ch. 6.1 - Sketch the region enclosed by the given curves....Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

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The work done to pump out the oil from the tank through the spout.

Solution Summary: The author calculates the work done to pump out the oil from the tank through the spout using the relation: lOB2=A.

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To calculate: The work done to pump out the oil from the tank through the spout.

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Chapter 6 Solutions