Question

Sodium fluoride is often added to municipal water supplies to support dental health. In a typical sys- tem, a tank of high-pressure sodium fluoride solution (η = 4.5 × 10−3 Pa · s) is connected through a narrow flow restricting tube to the main water flow. The flow- restriction tube is one meter long and has an internal diameter of 2 mm. The total water flow for through the main pipe is 2 m3/s and the fluoride solution should be added at a volume fraction of 3 × 10−5.

1. Find the pressure differential between the bottom of the tank and the water main required to achieve the necessary treatment rate.

2. If the flow-restricting tube undergoes un-noticed corrosion which decreases its radius by 40%, how will the fluoride levels be affected?

You may neglect the pressure differential from gravity along the flow-restricting tube.

Answer 1

Solution Given dato, 3 length of flow nYesErit tube . I internal diamele, di2mm otal weles fow though the main piPe, volume fraction of luonde Solution to be adde d hence, pressure diflerence betueer main wates supp aund flutside Solution lank to athieve fflow

2 12.8 dA hence dp = 6£7.gag kPa 45% theo fuss the Same dp Wege づ: hence f. 0-1296 자 hence foide n the wale becomes o. (26 f the 12.967. of ehe nitial onginal levels valve