Simplify Continuity and Momentum Equations for a Flowing Compressible Fluid

Question

A 1D steady, compressible flow is prescribed by the velocity profile: u = u(x), v = w = 0. The flow is inviscid (negligible viscous forces). Also, you may neglect gravity and other body forces.

1.    Simplify the form of the continuity equation by removing zero terms and show that one of the following statements is valid: ∂u/∂x + ∂v/∂y + ∂w/∂z = 0.
2.    Simplify the x, y and z momentum equations by removing zero terms and show that one of the following statements is valid: p+½pu² = const, p = const or p + pu² = const.

Summary

The question belongs to Mechanical Engineering and it is about a steady compressible flow prescribed by velocity profile. The continuity equation is to be simplified with momentum equations.

Note: The solution is in handwritten format.