Fluid Mechanics 9.1 - Derivation and Discussion of Differential Conservation of Momentum Equations

In this segment, we show step by step instructions on how to derive the conservation of momentum equation in the differential form. This equation is very important in that it is the basis of commonly used Euler and Naiver-Stokes Equations.
Errata: minute 17:39 should state yx not yy and 17:42 zx not zz. The rest of the video is correct and reflects yx and zx.
Module 9: The differential form of the Conservation of Momentum:
In module 6, we covered that the conservation of momentum can be derived from Newton's second law that states that the time rate of change of the linear momentum of the system = Sum of external forces acting on the system.
In module 9, we express this equation in the differential form, called the Euler's equations. We also introduce the alternative to Euler's equation for irrotational flow, Bernoulli's equation, which can be applied between any two points in the flow.
Student Learning Outcomes:
After completing this module, you should be able to:
1)Apply the Euler's and Bernoulli's (where applicable) equations to obtain pressure gradient and pressure differences between various points in the flow This material is based upon work supported by the National Science Foundation under Grant No. 2019664. Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

[@acaciajavanica3064]

Thanks Prof. This is very helpful

[@hebaalaaeldin2596]

Thank you so much, your explanation was awesome

[@shahidAhmad9430]

this was stunning explanation, thanks

[@chendanateegalapally7014]

Why didn't we consider the force due to pressure?

[@ethiotechamharic4921]

please solve this problem.a water jet is turned through an angle of 180 dgree by the device shown in figure.the fluid stream has a constant diameter of 2cm.if the magnitude of the restraining force is 500kpa,estimate the average water velocity of the incoming water jet.do you think this is a realistic set of flow condition?why or why not?

[@Mechanica55]

Not having pressure was a large omission.

[@CollegeFluidMechanics]

Please note that that "cube" is the size of one of your hairs, as this is a differential analysis. Hence, the pressure change is negligible for a small size and reasonable assumption in real life.