Conservation of Momentum: Momentum Theorem
In Newtonian mechanics, the conservation of momentum is defined by Newton’s second law of motion.
Newton’s Second Law of Motion
Newton’s Second Law of Motion
- The rate of change of momentum of a body is proportional to the impressed action and takes place in the direction of the impressed action.
- If a force acts on the body ,linear momentum is implied.
- If a torque (moment) acts on the body,angular momentum is implied.
Reynolds Transport Theorem
A study of fluid flow by the Eulerian approach requires a mathematical modeling for a control volume either in differential or in integral form. Therefore the physical statements of the principle of conservation of mass, momentum and energy with reference to a control volume become necessary.
This is done by invoking a theorem known as the Reynolds transport theorem which relates the control volume concept with that of a control mass system in terms of a general property of the system.
Statement of Reynolds Transport Theorem
The theorem states that "the time rate of increase of property N within a control mass system is equal to the time rate of increase of property N within the control volume plus the net rate of efflux of the property N across the control surface”.
Equation of Reynolds Transport Theorem
After deriving Reynolds Transport Theorem according to the above statement we get
(10.9) |
In this equation
N - flow property which is transportedη - intensive value of the flow property
Feel free to write