Fluid runs through a drainage pipe with a 10-cm radius and a length of 30 m (300 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. a. The pipe is 30 m long (3000 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. b. Determine how long it will take fluid at a point 9 cm from the center of the pipe to run the length of Me pipe. Round to 1 decimal place. c. Use regression to find a quadratic function to model the data. d. Use the model from part (c) to predict the velocity of the fluid at a distance 5.5 cm from the center of the pipe. Round tot decimal place.
Fluid runs through a drainage pipe with a 10-cm radius and a length of 30 m (300 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. a. The pipe is 30 m long (3000 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. b. Determine how long it will take fluid at a point 9 cm from the center of the pipe to run the length of Me pipe. Round to 1 decimal place. c. Use regression to find a quadratic function to model the data. d. Use the model from part (c) to predict the velocity of the fluid at a distance 5.5 cm from the center of the pipe. Round tot decimal place.
Solution Summary: The author calculates the time taken by the fluid to run the length of the pipe through the center using the tabular data.
Fluid runs through a drainage pipe with a 10-cm radius and a length of 30 m (300 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.
a. The pipe is 30 m long (3000 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.
b. Determine how long it will take fluid at a point 9 cm from the center of the pipe to run the length of Me pipe. Round to 1 decimal place.
c. Use regression to find a quadratic function to model the data.
d. Use the model from part (c) to predict the velocity of the fluid at a distance
5.5
cm from the center of the pipe. Round tot decimal place.
5
Use the method of disks to find the volume of the solid that is obtained
when the region under the curve y = over the interval [4,17] is rotated
about the x-axis.
3. Use the method of washers to find the volume of the solid that is obtained
when the region between the graphs f(x) = √√2 and g(x) = secx over the
interval ≤x≤ is rotated about the x-axis.
4. Use cylindrical shells to find the volume of the solid generated when the
region enclosed by the given curves is revolved about the x-axis.
y = √√x, y = 0, y = √√3
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