A town is installing a new 10” main to carry the drinking water. The only part remaining to be installed is a segment via the middle of town. Though, the excavators discover an archaeological site. The town decides to split the main into two parts, each looping around the site and re-connecting at the other end. The mayor decrees that ‘the velocity in each branch around the site shall be equivalent’. The town lays 800 feet of 6” pipe to the north of site and joins to the 10” main leading away from town. Though, the town then determines there is no more 6” pipe anywhere. The only pipe available is 8” pipe. The contractor, noting that ‘shall’ is a legally binding term whenever a contract is signed, should lay the proper amount of 8” pipe in such a way that the velocity in the two branches is the same. Find out:
a) The length of 8” pipe needed.
b) If rather, 800 feet of 8” pipe is laid parallel to the 6” pipe, the minor loss coefficient, K, for a valve which must be placed in the 8” line to exactly cause the velocities in two pipes to balance.
Suppose for purposes of solving this problem that turbulent flow exists and the resistance coefficients, f, for 6” pipe and 8’ pipe are 0.023 and 0.019, correspondingly.