Question

A doctor finds a partial blockage in a blood vessel. The flow speed in the region of the partial blockage is 5100 mm/hour. In a nearby vessel that is clear, the area is 0.51 mm2 . The blood flow speed, in mm/hr, in the clear region is 1200 mm/hr. What is the cross-section area, in mm2 , available for blood flow near the blockage

Answer 1

`0.12 mm^(2)`

Step-by-step explanation:

`v_(1)` = flow speed in the region of the partial blockage = 5100 mm/h

`v_(2)` = flow speed in the clear region of nearby vessel = 1200 mm/h

`A_(2)` = Cross-sectional area for the clear region = 0.51 mm²

`A_(1)` = Cross-sectional area for the region near the blockage

According to equation of continuity, Volume flow rate must remain same at all points. hence

`A_(1) v_(1) = A_(2) v_(2) \\A_(1) (5100) = (0.51) (1200)\\ A_(1) (5100) = 612\\\\ A_(1) = (612)/(5100) \\\\ A_(1) = 0.12 mm^(2)`