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Chapter 6: Q. 63 (page 557)

Find the hydrostatic force described in each of Exercises
61鈥�69.

The hydrostatic force exerted on one of the long sides of a giant rectangular hot tub that is 5feet wide, 8feet long, and 3 feet deep.

Short Answer

Expert verified

The hydrostatic force exerted on one of the long sides of a giant rectangular hot tub that is 5feet wide, 8feet long, and 3 feet deep is 4,000 pounds.

Step by step solution

01

Step 1. Given Information.

A rectangular hot tub that is 5feet wide, 8feet long, and 3 feet deep.

02

Step 2. Find Ak,dk.

Area of the rectangular tub=8鈭�y

Depth, dk=3-yk*

The density of the water is 蝇=62.4 pounds.

03

Step 3. Find the hydrostatic force.

The hydrostatic force is given by,

F=蝇Akdk鈮�62.4(8鈭�y)3-yk*=鈭�k=1n62.4(8)(3-yk*)鈭�y

F=鈭�08(62.4(8)(3-y))dy=500[3y-y22]08 =500[-8]=4000pounds

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