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Chapter 6: Q. 65 (page 557)

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

The hydrostatic force exerted by the water in a birdbath on its cylindrical side, given that the birdbath is in the shape of a cylinder that is 1 foot deep with a radius of 0.4 foot.

Short Answer

Expert verified

The hydrostatic force exerted by the water in a birdbath on its cylindrical side is 2 square feet.

Step by step solution

01

Step 1. Given Information.

The birdbath is in the shape of a cylinder that is 1 foot deep with a radius of 0.4 foot.

02

Step 2. Find Ak,dk

Area of the cylinderAk=2蟺(0.4)(1)=0.8蟺

Depth,dk=0.4-xk*

The density of the water is 62.4pounds.

03

Step 3. Find the hydrostatic force.

The hydrostatic force is given by,

F=蝇AKdk=62.4(0.8蟺鈭�y)0.4-yk*=鈭�k=1n62.4(0.8蟺)0.4-yk*(鈭�y)F=鈭�00.462.4(0.8(3.14))[0.4-y]dy=24.96蟺[0.4y-y22]00.4 =24.96蟺[0.08]鈮�2

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