Fluid runs through a drainage pipe with a 10cm radius and a

Fluid runs through a drainage pipe with a 10-cm radius and a length of 15 m (1500 cm). The velocity of the fluid gradually decreases from the center of the pipe toward the edges as a result of friction with the walls of the pipe, for the data shown,(a:) is the velocity of the fluid (in cm/sec) and x represents the distance (in cm) from the center of the pipe toward the edge The pipe is 15 m long (1500 cm). Determine how long it will take fluid to run the length of the pipe through the center of the pipe. Round to 1 decimal place. It will take fluid approximately the pipe. sec to run the length of the pipe through the center of the pipe.

Solution

I think we need to find the average velocity to find the approximate time

Vavg = summation ( V * Area ) / Total Area of cross section

Vavg = 195.3 * ( 1 - 0 ) + 194.8 ( 4- 1) + 193.8 (9 - 4) + 192.3 (16-9) + 190.3 (25-16) + 187.9 (36 -25) + 185 (49-36 ) + 181.7 (64-49) + 177 ( 81 - 64) / 81

Vavg = 185.35 cm/s

Hence it will take

T = 1500/185.35 sec = 8.1 sec