Potential flow dynamic pressure

For a fluid having a pressure P and flowing at speed v, the quantity ipv2 is known as the dynamic pressure and P+ipv2 is called the total pressure or the stagnation pressure. The pressure P of the flowing fluid is often called the static pressure, a potentially misleading name because it is not the same as the hydrostatic pressure. 

Use of the Potential Flow Equation of Motion to Calculate Dynamic Pressure... 

Steady-state analysis implies that the combination of fluid kinetic energy per unit volume and dynamic pressure is not time dependent. The potential flow equation of motion suggests that this combination of fluid kinetic energy per unit volume and dynamic pressure is not a function of any independent spatial variable. Consequently,... 

Hence, temperature profiles in pure isotropic solids, the scalar velocity potential for ideal fluid flow, and dynamic pressure profiles for flow through porous media are all based on the solution of Laplace s equation. Whenever the divergence of a vector vanishes and the vector is expressed as the gradient of a scalar, Laplace s equation is required to calculate the scalar profile. 

The latter approach is adopted because dynamic pressure gradients are calculated in the potential flow regime, outside the momentum boundary layer and far from the solid-liquid interface, where fi 0 and viscous forces are negligible. Then, 3P /3x is imposed across the boundary layer. This is standard practice for momentum boundary layer problems. Hence, if v represents the dimensionless velocity vector in the potential flow regime, then the steady-state dimensionless equation of motion is... 

There are no dimensionless numbers in this potential flow equation because convective forces per unit volume and dynamic pressure forces per unit volume both scale as pV /L. Furthermore, potential flow theory provides the formalism to calculate p and the dimensionless scalar velocity potential such that the vorticity vector vanishes and overall fluid mass is conserved for an incompressible fluid. Hence,... 

One concludes from (12-17a) and (12-17c) that neither 4> nor Vp is a function of the Reynolds number because Re does not appear in either equation. Consequently, dynamic pressure and its gradient in the x direction are not functions of the Reynolds number because Re does not appear in the dimensionless potential flow equation of motion, given by (12-16), from which /dx is calculated. In summary, two-dimensional momentum boundary layer problems in the laminar flow regime (1) focus on the component of the equation of motion in the primary flow direction, (2) use the equation of continuity to calculate the other velocity component transverse to the primary flow direction, (3) use potential flow theory far from a fluid-solid interface to calculate the important component of the dynamic pressure gradient, and (4) impose this pressme gradient across the momentum boundary layer. The following set of dimensionless equations must be solved for Vp, IP, u, and v in sequential order. The first three equations below are solved separately, but the last two equations are coupled ... 

The new set of dimensionless variables has transformed the equations of continuity and motion into two coupled partial differential equations for u and u with no explicit dependence on the Re5molds number because Re does not appear in either (12-21) or (12-22). Remember that is calculated from potential flow theory via (12-18c), exhibiting no dependence on Re, and x is the same as X. Hence, renormalization has no effect on the dimensionless dynamic pressure gradient in the x direction. One concludes from (12-21) and (12-22) that... 

Another potential problem is due to rotor instability caused by gas dynamic forces. The frequency of this occurrence is non-synchronous. This has been described as aerodynamic forces set up within an impeller when the rotational axis is not coincident with the geometric axis. The verification of a compressor train requires a test at full pressure and speed. Aerodynamic cross-coupling, the interaction of the rotor mechanically with the gas flow in the compressor, can be predicted. A caution flag should be raised at this point because the full-pressure full-speed tests as normally conducted are not Class IASME performance tests. This means the staging probably is mismatched and can lead to other problems [22], It might also be appropriate to caution the reader this test is expensive. 

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