You are trying to pump wastewater through a piping network then out a packed bed to filter out unnecessary impurities before returning it to its source. The bed is 0.98 m long, mean fluid velocity is 0.039 m/s, the void fraction is 0.52 , and the particle diameter is 142.1 microns. Water flows at 393.701 ft/min in the pipes, which has a fF of 0.01, the piping system has 2 standard elbows and the pipe ID is 0.10 m. The piping has 3 segments, with L1 = 7.34 ft and L3 = 3.66 ft. If the pressure losses through the pipes are half of the losses through the bed, what is the length of the vertical segment of the pipe in m? Assume that the impurities do not affect the properties of water, the process is in laminar flow in the bed, and turbulent in the piping. Ignore kinetic energy effects. Hint: Solve the packed bed first!

The correct answer is 21.22

L3 L2 L1