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f07_new_fall - Fluids Lecture 7 Notes 1 Momentum Flow 2...

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vector Fluids – Lecture 7 Notes 1. Momentum Flow 2. Momentum Conservation Reading: Anderson 2.5 Momentum Flow Before we can apply the principle of momentum conservation to a fixed permeable control volume, we must first examine the effect of flow through its surface. When material flows through the surface, it carries not only mass, but momentum as well. The momentum flow can be described as −→ −→ momentum flow = (mass flow) × (momentum / mass) where the mass flow was defined earlier, and the momentum/mass is simply the velocity vector vector V . Therefore −→ ˙ vector vector n A vector V momentum flow = m V = ρ V · ˆ V = ρ V n A vector vector n as before. Note that while mass flow is a scalar, the momentum flow is a where V n = V · ˆ vector, and points in the same direction as vector V . The momentum flux vector is defined simply as the momentum flow per area. −→ momentum flux = ρ V n V A n ^ m . m . V ρ V Momentum Conservation Newton’s second law states that during a short time interval dt , the impulse of a force vector F P applied to some affected mass, will produce a momentum change d vector a in that affected mass.
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