Confusing Proportion Question

Tutors: The question is as follows:
6) Pouisuille's law gives the rate, R, of a gas through cylindrical pipe in terms of the radius of the pipe, r, for a fixed drop in pressure between the two ends of the pipe.

a) Find a formula for Pouiseville's Law, given that the rate of the flow is proportional to the fourth power of the radius.

b) If R = 400 cm<sup>3</sup>/sec in a pipe of radius 3 cm for a certain gas, find a formula for the rate of flow of that gas through a pipe of radius r cm.

c) What is the rate of flow of the same gas through a pipe with a 5cm radius?
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psycho: This direct variation problem involves only algebra, as near as I can tell; you don't even need to use what you've learned in calculus. How far have you gotten?

Eliz.
 
If you've forgotten what you learned back in algebra, then review the lesson (in the blue hyperlink in my previous reply), and follow the example at the bottom of the page.

. . . . ."y varies directly as x": y = kx

. . . . ."y varies inversely as x": y = k/x

. . . . ."y varies jointly with x and z": y = kxz

Translate the statement in part (a) into the appropriate form above.

In part (b), they give you the values for one particular situation; use them to solve for k. This gives you the generic equation, which you use for the rest of the exercise.

In part (c), plug in "5" for the radius in the equation you derived in part (b).

Eliz.
 
I worked on the problem. Could you check to see if it's correct?

(a)
R=kr^4

(b)
R=kr^4
400=k(3)^4
4.938271605=k

R=4.938271605r^4

(c)
R=4.938271605r^4
R=4.938271605(5)^4
R=3086.419753 cm^3/sec

Now that I look at it, this problem isn't very difficult; it's just the way the word the problem around.
 
b) It would probably be better to leave k in "exact" form: k = 400/81.

c) Looks good to me.

Eliz.
 
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