Volume Flow Rate, Velocity, Factors

[karmatic]

Homework Statement

By what factor does the flow rate decrease when a water pipe of diameter 20 cm with a 10 cms^-1 flow rate, splits into two smaller pipes of diameters 11.54 cm and 16.33 cm?

Homework Equations

Q(volume flow rate)=(average velocity)(cross sectional area of flow)

The Attempt at a Solution

Q=(10cm/s^-1)(1/4*3.14*(20cm)^2)
Q=314.16cm^3/s

Q=(10cm/s^-1)(1/4*3.14*(11.54cm)^2)
Q=104.59cm^3/s

Q=(10cm/s^-1)(1/4*3.14*(16.33cm)^2)
Q=209.44cm^3/s

Just in case anyone is wondering, the "flow rate" stated in the problem question is actually the velocity (I had to clarify that with my teacher). I think I have the flow rates calculated correctly, but I am unsure of how to go about working out what factor the flow rate is decreasing by for each of the smaller pipes. The answer is a multiple choice question so it was a simple process of trial and error to work out which pair of factors worked for the problem, but is there a way of showing how I would work that out without the multiple choice aspect? I want to be able to show as much working as possible! Thanks in advance :)

 

[mikko196]

hey man I am actually doing teh same question how did u go about the guess and check to find out which one ?