Question

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, $v(x)$ 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.

$x$	0	1	2	3	4	5	6	7	8	9
$v(x)$	195.3	194.8	193.8	192.3	190.3	187.9	185.0	181.7	177.8	173.5

part 0 / 4
part 1 of 4
(a) 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 sec to run the length of the pipe through the center of the pipe.

Explanation:

Step1: Identify the velocity at the center

When $x = 0$ (center of the pipe), $v(0)=195.3$ cm/sec.

Step2: Use the formula $t=\frac{d}{v}$

The length of the pipe $d = 1500$ cm and $v = 195.3$ cm/sec. So $t=\frac{1500}{195.3}$.

Step3: Calculate the time

$t=\frac{1500}{195.3}\approx7.7$ sec.

Answer:

$7.7$