What is the average radius of the pipe within the hill?

[jinman]

Homework Statement

An old two pipe system runs through a hill, with distances D_a=D_b=30m and the total Distance is D=110m. On each side of the hill, the pipe radius is .0200m. However, the radius of the pipe inside the hill is no longer known. To determine it, hydraulic engineers first establish that the water flows through the left and right sections at 2.50m/s. Then they release a dye in the water at point A and find that it takes 88.8s to reach point B. What is the average radius of the pipe within the hill (sorry i don't have a diagram)?

Homework Equations

AoVo=AV

v=d/t

The Attempt at a Solution

I cut this problem in half to try and make it work. I used AoVo=AV where Ao is the little pipe, and A is the the middle pipe.

AoVo=AV>>>>(pi_r^2)(2.50m/s)=(pi_r^2)(V)

solve for r^2 on right

(pi_r^2)(2.50m/s)=(pi_r^2)(d/t)>>>>sq. root(.02^2)(2.50m/s)(44.4s) / 55m= .03m

i know i am going wrong in many places. Any suggestions?

 

[kamerling]

The method used seems Ok, but I can't tell where the distance of 55m you used comes from, nor do I understand why you use 44.5s instead of 88.8s. I thought d was the lenth of the pipe in the hill and t the time it for the dye to go through this pipe?

 

[jinman]

I used 55m because D=110m is the the whole system, so i looked at the first half. which is why i used 44.4 seconds. Is this the right to do the problem?