In the chapter on head loss, it was determined that both major losses and minor losses in piping systems are proportional to the square of the flow velocity. The system head loss must be directly proportional to the square of the volumetric flow rate because the volumetric flow rate is directly proportional to the flow velocity.

It must be added that the open hydraulic systems contain not only the friction head but also the elevation head, which must be considered. The elevation head (static head) represents the potential energy of a fluid due to its elevation above a reference level.

In many cases, the total head of a system is a combination of elevation head and friction head, as shown in the figure.

In nuclear engineering most of hydraulic systems are closed hydraulic loops and these systems only have friction head (no static head).

Major Head Loss - Friction Loss

## Summary:

• Head loss of the hydraulic system is divided into two main categories:
• Darcy’s equation can be used to calculate major losses.
• The friction factor for fluid flow can be determined using a Moody chart.
• The friction factor for laminar flow is independent of the roughness of the pipe’s inner surface. f = 64/Re
• The friction factor for turbulent flow depends strongly on the relative roughness. The Colebrook equation determines it. It must be noted that the friction factor is independent of the Reynolds number at very large Reynolds numbers.

References:
Reactor Physics and Thermal Hydraulics:
1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
5. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.
10. White Frank M., Fluid Mechanics, McGraw-Hill Education, 7th edition, February, 2010, ISBN: 978-0077422417

## See above:

Centrifugal Pumps