However, I am currently wondering what the 'use' is for this approximation. I remember during my bachelor's degree in physics lessons that we were taught that this approximation was useful as the incompressible version was 'easier' for computing (by hand) exact solutions in specific cases like pipe flow. This just seemed intuitive to me at the time, as there were of course fewer terms.

While it is true that the incompressible assumption circumvents challenging aspects such as shocks and reduces the number of unknowns, it introduces a host of other issues. In my opinion, these can often be just as difficult (or more so) to overcome as the unique issues encountered in compressible flows. A simple analog for incompressible flows is to think back to statically indeterminate beams from a statics course. Both are overconstrained, which prevent any straightforward computation of the internal forces.

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Anyway, I think the proper answer to your question of which is harder is that it depends. They each have their own unique challenges, but I think it is wrong to say one is always more difficult than the other. Transonic flows around a complex vehicle might be very difficult to solve compared to a relatively slow incompressible pipe flow. However, a fully-enclosed incompressible flow can pose more difficult challenges than a supersonic flow past a simple geometry.

When a laser beam of high intensity interacts with a dense material, an ablation front appears in the high-temperature plasma resulting from the interaction. Such a front can be used to accelerate and compress the dense material. The dynamics of the ablation front is strongly coupled to that of the absorption front where the laser energy is absorbed. The present paper determines analytical solutions of the front internal structure in the fully compressible case.

Prerequisite: ME 390. Prediction of aerodynamic forces due to subsonic flows over aircraft/missile wings and bodies. Calculation of pressure distribution, lift, drag, moments and wall-shearing stress in incompressible flow. Compressibility corrections are considered. Impact of these calculations on aerodynamic design are evaluated.

Prerequisite: ME 390. Second-semester fluids course with applications to systems of engineering interest. Potential flows, boundary layers, duct flows, lubrication theory, lift and drag. 1-dimensional compressible flow with area change, friction, heating/cooling, normal shock waves, oblique shock waves and Prandtl-Meyer expansions. Both numerical and analytical solution techniques are explored.

Prerequisite: ME 390. Fundamental principles of incompressible fluid flow and their applications to pipe flow, open channel flow and the performance of hydraulic turbomachines. Flow in pipe systems ranging from simple series systems to complex branched networks. Uniform flows, gradually varying flows, rapid transitions and hydraulic jumps in open channels. Performance of radial, mixed-flow and axial flow centrifugal pumps and turbines, and of impulse turbines.

Prerequisites: Background equivalent to a two semester undergraduate course sequence in fluid mechanics; Enrollment for graduate students only. Corequisite: ME 501A or equivalent. Derivation of conservation equations from fundamental principles and the constitutive relations for Newtonian fluids. Exact solutions of the Navier-Stokes equations, including transient and oscillatory solutions. Laminar and turbulent boundary layers as well as Stokes flow solutions. Introduction to the vorticity equation and vortex dynamics. Potential flow applications.

Prerequisites: Background equivalent to a two semester undergraduate course sequence in fluid mechanics; Enrollment for graduate students only. Corequisite: ME 501A or ME 501B. Fundamental treatment of compressible flows including generalized one-dimensional flows, normal and oblique shock waves, Prandtl-Meyer expansion waves, unsteady waves, linearized potential flow. Method of characteristics. Hypersonic flow, high temperature and low density effects.

Stagnation conditions and properties. Quasi-1D compressible flows in ducts. Planar nonlinear waves: adiabatic and nonadiabatic normal shocks, oblique shocks, detonations and deflagrations, shock tubes.

Governing equations, velocity potential and stream function. Planar potential flows: complex analysis formulation; elementary separable solutions and superposition, flow forces and moments, flow around a cylinder, flow transformations and solutions by conformal and analytic mappings; flat plate, linear and radial cascade flows. Axisymmetric ideal potential flows; elementary separable solutions and superposition. Unsteady flows and apparent mass forces. Planar and axisymmetric free surface waves, Rayleigh-Taylor instabilities. be457b7860

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