What is Reynolds transport theorem for Conservation of Mass with deformable control volume?

Reynolds transport theorem states that the rate of change of an extensive property N, for the system is equal to the time rate of change of N within the control volume and the net rate of flux of the property N through the control surface.

What is conservation of momentum in fluid mechanics?

Conservation of Momentum: Newton’s second law is simply the law of conservation of momentum. It states that the time rate of change of momentum of a system of particles is equal to the sum of external forces acting on that body.

What is the main purpose of Reynolds Transport Theorem?

The Reynolds transport theorem is a very powerful mathematical relation often used in advanced engineering courses. Can you use it to visualize the difference between a Lagrangian (closed system of fixed mass) and a Eulerian (open system of variable mass) fluid momentum rate balance analysis where X = mV? a.

What is the relationship between the Reynolds transport theorem and the material derivative?

19. What is the relationship between the Reynolds transport theorem and the material derivative? A. The Reynolds transport theorem is the integral equivalent of the material derivative.

What is the name of the equation that relates the system and control volume form of the continuity energy and linear momentum equations?

Euler equations (fluid dynamics)

What is RTT in fluids?

Reynolds Transport Theorem (RTT) • An analytical tool to shift from describing the. laws governing fluid motion using the system. concept to using the control volume concept.

What is the momentum conservation equation?

The formula for the Law of Conservation of Momentum is p=p’ or m1v1+m2v2=m1v1’+m2v2′. This equation shows us that the sum of the momentum of all the objects in the system is constant.

What is the law governing momentum equation?

Explanation: Momentum equation is derived using Newton’s second law of motion. Explanation: According to newton’s second law, force is equal to the product of mass and acceleration, where force and acceleration are vector quantities (\vec{F}=m\vec{a}).

Which of these terms represent convection in the momentum equation?

Explanation: : From general conservation equation, the convection term is div(ρuΦ). For momentum equation, \Phi=\vec{V}. So, the convection term in momentum equation is div(ρu\vec{V}).

What is material derivative in fluid mechanics?

The material derivative computes the time rate of change of any quantity such as temperature or velocity (which gives acceleration) for a portion of a material moving with a velocity, v . If the material is a fluid, then the movement is simply the flow field.

What is Euler’s equation of motion in fluid mechanics?

Euler’s equation for a steady flow of an ideal fluid along a streamline is a relation between the velocity, pressure, and density of a moving fluid. It is based on Newton’s Second Law of Motion. The integration of the equation gives Bernoulli’s equation in the form of energy per unit weight of the following fluid.