Exam (16).pdf - Question The velocity profile v(r for turbulent flow in smooth pipes is sometimes estimated by the seventh-root law originally proposed

# Exam (16).pdf - Question The velocity profile v(r for...

This preview shows page 1 - 6 out of 6 pages.

Question: The velocity profile, v ( r ), for turbulent flow in smooth pipes is sometimes estimated by the seventh-root law, originally proposed by Blasius (1913): where V 0 is the maximum (centerline) velocity and R is the radius of the pipe. Estimate the energy and momentum correction factors corresponding to the seventhroot law. Answer : The velocity distribution in the pipe can be expressed as follows: â€¦â€¦ (1) Here, r is the distance from the center line of the pipe, is the center line (maximum) velocity, R is the radius of the pipe. Area of the pipe can be expressed as follows: â€¦â€¦ (2) Kinetic energy correction factor can be expressed as follows:
Equation (4) can be written as follows: â€¦â€¦ (3) Combine Equation (1) and (2) with Equation (3). Express the value of as follows: â€¦â€¦ (4) To facilitate integration: â€¦â€¦ (5) Equation (5) can be modified as follows: â€¦â€¦ (6) Differentiate Equation (6) with respect to

#### You've reached the end of your free preview.

Want to read all 6 pages?

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern