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[DB]

proportionality help needed please

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%?
$$p\propto \frac{1}{d^6}$$

$$\frac{p_2}{p_1}=\frac{1}{0.2^6}$$

$$\frac{p_2}{p_1}=15625$$

therefore

$$\frac{15625}{1}\equiv \frac{1}{0.2^6}$$

so

$$\Delta X_m=15625$$

and

$$\Delta X_m -1 = \Delta X_{relative}$$

and

$$\Delta X_{rel.} * 100 = Delta X_%$$

so

$$15625-1=15624*100=\Delta X_%$$

$$\Delta X_% = 1.5624 * 10^6$$?
i must of done something wrong...any help appreciated

 

[DB]

if u can't see my last three step i got the percentage change as 1.5624*10^6%

 

[Doc Al]

$$p\propto \frac{1}{d^6}$$

$$\frac{p_2}{p_1}=\frac{1}{0.2^6}$$

Recheck this step. When the diameter decreases by 20%: $D_2 = 0.8 D_1$

 

[DB]

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?

 

[Doc Al]

Sounds good to me.

 

[DB]

thanks doc