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Proportionality help needed

  • Thread starter DB
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  • #1
DB
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proportionality help needed plz

stuck on a proportionality problem...
1) the pressure exerted by a fluid in a pipe varies inversely as the sixth power of the diameter. what is the multiplicative change (delta X_m) and percentage change (delta X%) in the pressure is the diameter of the pipe decreases by 20%?
[tex]p\propto \frac{1}{d^6}[/tex]

[tex]\frac{p_2}{p_1}=\frac{1}{0.2^6}[/tex]

[tex]\frac{p_2}{p_1}=15625[/tex]

therefore

[tex]\frac{15625}{1}\equiv \frac{1}{0.2^6}[/tex]

so

[tex]\Delta X_m=15625[/tex]

and

[tex]\Delta X_m -1 = \Delta X_{relative}[/tex]

and

[tex]\Delta X_{rel.} * 100 = Delta X_%[/tex]

so

[tex]15625-1=15624*100=\Delta X_%[/tex]

[tex]\Delta X_% = 1.5624 * 10^6[/tex]?
i must of done something wrong...any help appreciated :smile:
 

Answers and Replies

  • #2
DB
501
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if u cant see my last three step i got the percentage change as 1.5624*10^6%
 
  • #3
Doc Al
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DB said:
[tex]p\propto \frac{1}{d^6}[/tex]

[tex]\frac{p_2}{p_1}=\frac{1}{0.2^6}[/tex]
Recheck this step. When the diameter decreases by 20%: [itex]D_2 = 0.8 D_1[/itex]
 
  • #4
DB
501
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thanks doc
shame on me, stupid mistake, but this seems right, the multiplicative change is 3.18 and the percentage change is 218%. that right?
 
  • #5
Doc Al
Mentor
44,867
1,114
Sounds good to me.
 
  • #6
DB
501
0
thanks doc
 

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