For fluid flow in pipes, friction is described by a dimensionless number, the Fanning friction factor (f). The Fanning friction factor is dependent on a number of parameters related to the size of the pipe and the fluid, which can all be represented by another dimensionless quantity, the Reynolds number (Re). A formula that predicts f given Re is the von Karman equation: 7= 4 log10 (Re/7) – 0.4 Typical values for the Reynolds number for turbulent flow are 10,000 to 500,000 and for the Fanning friction factor are 0.001 to 0.01. a) Develop a function that uses bisection to solve for f given a user-supplied value of Re between 2,500 and 1,000,000. b) Design the function so that it ensures that the absolute error in the result is less than 0.000005 c) What is the value (or closest value) of absolute error (unto 4 decimal points) after the 3rd iterations at
For fluid flow in pipes, friction is described by a dimensionless number, the Fanning friction factor (f). The Fanning friction factor is dependent on a number of parameters related to the size of the pipe and the fluid, which can all be represented by another dimensionless quantity, the Reynolds number (Re). A formula that predicts f given Re is the von Karman equation: 7= 4 log10 (Re/7) – 0.4 Typical values for the Reynolds number for turbulent flow are 10,000 to 500,000 and for the Fanning friction factor are 0.001 to 0.01. a) Develop a function that uses bisection to solve for f given a user-supplied value of Re between 2,500 and 1,000,000. b) Design the function so that it ensures that the absolute error in the result is less than 0.000005 c) What is the value (or closest value) of absolute error (unto 4 decimal points) after the 3rd iterations at
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![For fluid flow in pipes, friction is described by a dimensionless number, the Fanning friction factor (f). The Fanning friction factor is dependent on a number of parameters related to the size of the pipe and the fluid, which can all be represented by another dimensionless quantity, the Reynolds number (Re). A formula that predicts f given Re is the von Karman equation:
\[
\frac{1}{\sqrt{f}} = 4 \log_{10} \left( \frac{Re}{\sqrt{f}} \right) - 0.4
\]
Typical values for the Reynolds number for turbulent flow are 10,000 to 500,000 and for the Fanning friction factor are 0.001 to 0.01.
a) Develop a function that uses **bisection** to solve for f given a user-supplied value of Re between 2,500 and 1,000,000.
b) Design the function so that it ensures that the absolute error in the result is less than 0.000005.
c) What is the value (or closest value) of absolute error (up to 4 decimal points) after the 3rd iteration at Re = 10,000. Use the typical values of the Fanning factor as the initial guesses for the bisection methods.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa437b1f1-94c0-462c-9640-81b3f97959f1%2F2c51eb9f-49a9-499a-93a1-b91ebcb191dd%2Fo71w6z_processed.png&w=3840&q=75)
Transcribed Image Text:For fluid flow in pipes, friction is described by a dimensionless number, the Fanning friction factor (f). The Fanning friction factor is dependent on a number of parameters related to the size of the pipe and the fluid, which can all be represented by another dimensionless quantity, the Reynolds number (Re). A formula that predicts f given Re is the von Karman equation:
\[
\frac{1}{\sqrt{f}} = 4 \log_{10} \left( \frac{Re}{\sqrt{f}} \right) - 0.4
\]
Typical values for the Reynolds number for turbulent flow are 10,000 to 500,000 and for the Fanning friction factor are 0.001 to 0.01.
a) Develop a function that uses **bisection** to solve for f given a user-supplied value of Re between 2,500 and 1,000,000.
b) Design the function so that it ensures that the absolute error in the result is less than 0.000005.
c) What is the value (or closest value) of absolute error (up to 4 decimal points) after the 3rd iteration at Re = 10,000. Use the typical values of the Fanning factor as the initial guesses for the bisection methods.
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