The figure shows two sections of an old pipe system that runs through a hill. Th

Question

The figure shows two sections of an old pipe system that runs through a hill. The overall length from point A to point B isD. On each side of the hill, the two sections dA and dB both have length d and radius r. However, the radius of the pipe inside the hill is no longer known. To determine it, hydraulic engineers first establish that water flows through the left and right sections at the same speed v. Then they release a dye in the water at point A and find that it takes time T to reach point B. What is the average radius of the pipe within the hill? Express your answer in terms of d, r, v, D, and T.

The figure shows two sections of an old pipe system that runs through a hill. The overall length from point A to point B isD. On each side of the hill, the two sections dA and dB both have length d and radius r. However, the radius of the pipe inside the hill is no longer known. To determine it, hydraulic engineers first establish that water flows through the left and right sections at the same speed v. Then they release a dye in the water at point A and find that it takes time T to reach point B. What is the average radius of the pipe within the hill? Express your answer in terms of d, r, v, D, and T.

Explanation / Answer

r*Sqrt(V/((D-2d)/(T-(2d/v))))

In words you end up with r times the square root of Velocity divided by ((D-2d)/(T-(2d/v)))

I don't do so well with words.

Hope this helps.

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