The momentum equation, in the context of fluid mechanics, relates the net force acting on a fluid system to the rate of change of momentum. It is derived from Newton’s second law of motion, which states that the rate of change of momentum of an object is equal to the net force acting on it. In fluid mechanics, this principle is applied to fluid elements instead of solid objects. The momentum equation can be expressed in vector form as:

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where:

• $\text{Net force}$ is the vector sum of all external forces acting on the fluid element.
• $m$ is the mass of the fluid element.
• $V$ is the velocity vector of the fluid element.
• $t$ is time.