   Chapter 8.3, Problem 19E

Chapter
Section
Textbook Problem

A metal plate was found submerged vertically in seawater, which has density 64 lb/ft3. Measurements of the width of the plate were taken at the indicated depths. Use Simpson’s Rule to estimate the force of the water against the plate. To determine

To estimate: The force of the water against the plate using Simpson’s Rule.

Explanation

Given:

The density of water is δ=64lb/ft3.

The depth and width of the plate as shown in Table 1:

The number of subintervals as n=7.

Calculation:

The width of the plate is measured at equal interval of depth. Hence, the subinterval width (Δx) is 0.4.

Calculate the force of the water against the plate using Simpson’s Rule:

F=Δxδ3[x1w1(x1)+4x2w2(x2)+2x3w3(x3)+4x4w4(x4)+2x5w5(x5)+4x6w6(x6)+x7w7(x7)] (1)

Substitute 0.4 for Δx, 7.0 for x1, 7.4 for x2, 7.8 for x3, 8.2 for x4, 8.6 for x5, 9.0 for x6, and 9.4 for x7 in Equation (1).

F=0.4δ3[7.0w1(7.0)+4×7.4w2(7.4)+2×7.8w3(7.8)+4×8.2w4(8.2)+2×8.6w5(8.6)+4×9.0w6(9.0)+9.4w7(9.4)]=0

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