D.E. Problem Explained: Limits and Units

ehrenfest · May 25, 2008

[SOLVED] D.E. problem

Homework Statement

See the attachment.

Homework Equations

The Attempt at a Solution

dh/dt = 1/100 - 1/4h

Why is the limit not h = 1/25 or 4 cubic feet?

HallsofIvy · May 25, 2008

Please be careful about parentheses! I had first interpreted "1/4h" as "1/(4h)" and got a silly answer!

However, your equation is wrong. Since water comes in at 1 cubic foot per second and the "water tower" has a uniform cross section area of 100 square feet, yes, that causes the water level to rise at 1/100 feet per second which are the correct units for dh/dt.

But the water is also going out at (1/4)t cubic feet per second which is NOT the correct units. If water is going out at (1/4)t cubic feet per second, how fast is the water level dropping in feet per second?

D.E. Problem Explained: Limits and Units

Homework Statement

Homework Equations

The Attempt at a Solution

Attachments

Discussion

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D.E. Problem Explained: Limits and Units

Homework Statement

Homework Equations

The Attempt at a Solution

Attachments

Discussion

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