Notes on Momentum Eqn.

## Quality in Applying the Momentum Equation

What quality looks like.

• The right CV is defined and sketched & described (as appropriate). Inlet/Exit ports are labeled.
• New! Coordinate axis defined & sketched. The reference frame is defined (as needed).
• New! A Force Diagram (FD) is sketched and labeled (separate sketch from MD & situation sketch).
• New! A Momentum Diagram (MD) is sketched & labeled (separate sketch from FD & situation sketch).
• The general equations is written down and reduced so that it applies to the problem at hand; key details of analysis are shown.
• New! Either vectors are used OR scalars are used (no mixing up of vectors and scalars)
• If force (vector) is the goal, your answer specifies magnitude & direction.

Actions to achieve quality (step by step process)

• See text p. 168.

## Reference Frame (RF)

A reference frame is a three-dimensional frame work from which an observer measures position, velocity, etc.

If the reference frame is accelerating, it is called a non-inertial reference frame. In this ref. frame, F = ma needs to be re-derived to account for the acceleration. For example, if you place your RF (and observer) on a rocket that is taking off, this is a non-inertial RF because the RF is accelerating relative to a ground-based reference frame.

If a reference frame is not accelerating, the reference frame is called an inertial reference frame.

Ground based reference frame. A RF fixed to the earth. This is an inertial RF. Not commonly labeled.

When objects are moving, example a jet-powered car, the easiest soln approach is to place the RF on the moving vehicle. However, if the RF is accelerating, then the formulation of the momentum eqn. used in our text is not valid.

## Vector Eqns versus Scalar Eqns

The momentum equation is the first vector equation we will use in this course. In mathematics, a vector eqn. is one whose terms are vectors (not scalars).

All previous eqns. (e.g. Bernoulli, Flow Rate, Continuity, ….) are scalar eqn because the terms in these equations are scalar valued (not vector valued.

Very important to understand the differences between vector and scalar eqns and to use proper notation when writing eqns

Tips

• A vector eqn can be represented using 1, 2, or 3 scalar eqns. For example, one in the i-hat direction, one in the j-hat direction, and one in the k-hat direction.
• When writing down an eqn, use vectors or use scalars. Do not write some terms as vectors and some terms as scalars.
• When applying the momentum eqn., pick the coordinate direction that makes solution of the problem the easiest.