Determine the length of pipe necessary for the pipe system.

A town is installing a new 10" main to carry drinking water. The only section remaining to be installed is a segment throughout the middle of town. Though, the excavators discover an archaeological site. The town decides to split the key into two sections, each looping around the site and reconnecting at the other end. The mayor decrees that "the velocity in each branch around the site shall be equal". The town lays 800 feet of 6" pipe to the north of the site and connects to the 10" main leading away from town. However, the town then finds out there is no more 6" pipe. Anywhere. The only pipe available is 8" pipe. The contractor, noting that "shall" is a legally binding term when a contract is signed, must lay the proper amount of 8" pipe such that the velocity in the two branches is the same. Find out: a) length of 8" pipe required, b) if instead, 800 feet of 8" pipe is laid parallel to the 6" pipe, minor loss coefficient, K, for a valve that must be placed in the 8" line to exactly cause the velocities in the two pipes to balance. Suppose for purposes of solving this problem that turbulent flow exists and the resistance coefficients, f, for the 6" pipe and 8' pipe are 0.023 and 0.019, correspondingly.