1. Pharos University ME 259 Fluid Mechanics Lecture # 5 Dr. A. Shibl Momentum Equation

2. Basic Laws Conservation of mass: dM/dt=0 for system ∂/∂t ∫ ϱ d + ∫ ϱ ⊽. d Ᾱ =0 for control vol. Newton’s 2 nd law Σ F = ma Σ F = ∂/∂t ∫ ⊽ ϱ d + ∫ ⊽ ϱ ⊽. d Ᾱ 8-Dec-15 2/27

3. Momentum Analysis of Flow Systems

4. Newton’s Laws Newton’s laws: –First law: a body at rest remains at rest, and a body in motion remains in motion at the same velocity in a straight path when the net force acting on it is zero. –Second law: the acceleration of a body is proportional to the net force acting on it and is inversely proportional to its mass. – Third law: when a body exerts a force on a second body, the second body exerts an equal and opposite force on the first.

5. Choosing a Control Volume Fixed, and moving. –For moving CV, use relative velocity,

6. Body and Surface Forces

7. Basic Laws for a System Momentum Equation for Inertial Control Volume

8. Basic Law, and Transport Theorem

9. Linear Momentum Equation Use RTT to shift from system formulation of the control volume formulation

10. Momentum Equation for Inertial Control Volume

11. Special Cases Steady Flow Average velocities

12. Basic Laws for a System The Angular-Momentum Principle

13. Basic Law, and Transport Theorem

14. The Angular-Momentum Principle

15. c04u013

16. c04u014

17. c04u015

18. c04u016

19. c04u017

20. c04u018

21. c04u019

22. c04u020

23. c04u021

24. c04u022

25. c04u023

26. c04u028

27. c04u029

28. c04u030

29. c04u031

30. c04u032