Fluid runs through a drainage pipe with a 10-cm radius and a length of 30 m (3000 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 v ( x ) 195.6 195.2 194.2 193.0 191.5 x 5 6 7 8 9 v ( x ) 189.8 188.0 185.5 183.0 180.0 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 the 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 to 1 decimal place.
Fluid runs through a drainage pipe with a 10-cm radius and a length of 30 m (3000 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 v ( x ) 195.6 195.2 194.2 193.0 191.5 x 5 6 7 8 9 v ( x ) 189.8 188.0 185.5 183.0 180.0 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 the 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 to 1 decimal place.
Solution Summary: The author calculates the time taken by the fluid to run the length of a drainage pipe through the center of the pipe.
Fluid runs through a drainage pipe with a 10-cm radius and a length of 30 m (3000 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
v
(
x
)
195.6
195.2
194.2
193.0
191.5
x
5
6
7
8
9
v
(
x
)
189.8
188.0
185.5
183.0
180.0
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 the 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 to 1 decimal place.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning