Chapter 5.R, Problem 30E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

A steel tank has the shape of a circular cylinder oriented vertically with diameter 4 m and height 5 m. The tank is currently filled to a level of 3 m with cooking oil that has a density of 920 kg/m3. Compute the work required to pump the oil out through a 1-meter spout at the top of the tank.

To determine

**To compute:**

The work required to pump the oil out of the tank.

Explanation

**1) Given:**

Diameter of cylinder is

Height of cylinder is

Density of oil is

**2) Calculations:**

The volume of a horizontal slice of cooking oil having

That is,

Density of oil is

Therefore,

Mass of slice is

Weight is

Now, the height of the cylinder is

Also, the cylinder is filled to a level of

Thus, to calculate the total work needed to empty the tank, integrate the weight from

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