What is the integral form of momentum equation?
1 Momentum Integral Equation. ∂ ∂ x [ ϱ u ( u e – u )|+ ∂ ∂ y [ ϱ v ( u e – u )]+ d u e d x ( ϱ e u e – ϱ u) =- ∂ ∂ y ( μ ∂ u ∂ y – ϱ u ′ v ′ ¯ ) .
How is momentum equation derived?
The momentum equation is a statement of Newton’s Second Law and relates the sum of the forces acting on an element of fluid to its acceleration or rate of change of momentum. You will probably recognise the equation F = ma which is used in the analysis of solid mechanics to relate applied force to acceleration.
What is the derivation of momentum?
Derivation of Conservation of Momentum Newton’s third law states that for a force applied by an object A on object B, object B exerts back an equal force in magnitude, but opposite in direction. This idea was used by Newton to derive the law of conservation of momentum.
How do you write a momentum equation?
Momentum Equation (Newton’s Second Law of Motion) The left side, ρ ( ∂ v / ∂ t + v ∂ v / ∂ x ) , is mass times acceleration per unit volume of fluid (there is a velocity change in time, , as well as a change as it moves in distance, ).
What is integral form?
The integral form of the full equations is a macroscopic statement of the principles of conservation of mass and momentum for what is called a control volume. A control volume is a conceptual device for clearly describing the various fluxes and forces in open-channel flow.
What is the derivation and unit of momentum?
Momentum is a vector quantity and is defined as the product of the mass and velocity of a moving body. Momentum is mathematically represented as, p = mass (m) x velocity (v). It is measured in kg-m/s in the SI unit.
What is the derivation of formula?
The derivative measures the steepness of the graph of a given function at some particular point on the graph. Thus, the derivative is also measured as the slope. It means it is a ratio of change in the value of the function to change in the independent variable.