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Drag force and drag coefficient
Published in Mohammad H. Sadraey, Aircraft Performance, 2017
As a fluid is compressible, the flow of fluid may be compressible too. Incompressible flow is a flow where the density is assumed to be constant throughout. Compressible flow is a flow in which the density varies. A few important examples are the internal flow through rocket and gas turbine engines, high-speed subsonic, transonic, supersonic, and hypersonic wind tunnels, the external flow over modern airplanes designed to cruise faster than Mach 0.3, and the flow inside the common internal combustion reciprocating engine. For most practical problems, if the density changes by more than 5%, the flow is considered to be compressible. Figure 3.20 shows the effect of compressibility on drag for three configurations.
Force-System Resultants and Equilibrium
Published in Richard C. Dorf, The Engineering Handbook, 2018
Compressible flow is defined as variable density flow; this is in contrast to incompressible flow, where the density is assumed to be constant throughout. The variation in density is mainly caused by variations in pressure and temperature. We sometimes call the study of such fluids in motion gas dynamics. Fluid compressibility is a very important consideration in modern engineering applications. Knowledge of compressible fluid flow theory is required in the design and operation of many devices commonly encountered in engineering practice. A few important examples are the external flow over modern highspeed aircrafts; internal flows through rocket, gas turbine, and reciprocating engines; flow through natural gas transmission pipelines; and flow in high-speed wind tunnels.
Units and Significant Figures
Published in Patrick F. Dunn, Fundamentals of Sensors for Engineering and Science, 2019
An engineering student measures an ambient lab pressure and temperature of 405.35 in. H2O and 70.5 °F, respectively, and a wind tunnel dynamic pressure (using a pitot-static tube) of 1.056 kN/m2. Assume that Rair = 287.04 J/(kg · K). Determine with the correct number of significant figures (a) the room density using the perfect gas law in SI units (state the units with the answer) and (b) the wind tunnel velocity using Bernoulli’s equation in units of ft/s. Bernoulli’s equation states that for irrotational, incompressible flow the dynamic pressure equals one-half the product of the density times the square of the velocity.
Numerical modeling of the performance of high flow DMAs to classify sub-2 nm particles
Published in Aerosol Science and Technology, 2019
Huang Zhang, Girish Sharma, Yang Wang, Shuiqing Li, Pratim Biswas
Figure 2 shows the change in Mach number (M2) and gas velocity (u2) in the working section as a function of the sheath flow rate (Q). Owing to the translation of random thermal energy () into directed kinetic energy () as the gas is accelerated to high velocity by a large pressure drop, the temperature (T) and density (ρ) change while the mass is conserved. As a result, Mach number and velocity do not vary in the same way, and the curves deviate from one another. The incompressible flow is defined as the regime where resulting density and temperature change are sufficiently small that they can be neglected. The consideration of temperature is important here, because it determines the speed of sound, which is the normalizing factor used in calculating the Mach number (M). Figure 2 also points out for the incompressible flow regime, i.e. M < 0.3, Q should be less than 368 lpm. The highest flow rate simulated in this work is 230 lpm, thus validating the incompressible flow regime assumption. This value of sheath flow rate used is consistent with several experimental studies (Fang et al. 2014; Wang et al. 2014, 2015, 2017; Carbone et al. 2016; Cai et al. 2018). On the other hand, there are several studies where the maximum reported value of Q (Qmax_rep) is about 740 lpm (de la Mora 2011); thus requiring compressible flow simulations. This is the subject of a following paper to be done by the authors.
The influences of Doppler shift on the wave dissipation and soil responses over the porous medium
Published in Coastal Engineering Journal, 2018
Jing-Hua Lin, Hung-Chu Hsu, Yang-Yih Chen
The assumption of incompressible flow indicates the density of a fluid particle retains the constant in moving along the streamline, i.e. the material derivative is zero, . In addition, the external flow outside of the boundary layer is discussed in the present article, hence, the viscosity of fluid can be neglected. In the wave motion, the assumptions of incompressible and inviscid flow are usually obeyed. It also indicates that the fluid viscosity induced the energy dissipation inside the boundary layer is omitted in the study. In fact, the velocity defect inside the boundary layer is influenced by the slip velocity which exists at the soil-fluid interface (Lin et al. 2013). The assumption of a rigid porous media means that the soils retain the static state and the seabed is not subject of deformation. The common specific weight of sandy soils 2.65~2.75 are larger than that of water, so it is reasonable to consider as a rigid seabed before the threshold movement is occurred (Chen et al. 2012). It means that the interaction between wave displacements and seabed deformation is not considered. On the other hand, the soils of the same size are arranged by the wave sorting, hence, the porous medium is quite close to an isotropic and homogeneous material (Chen et al. 2012).
Size effect on compressible flow and heat transfer in microtube with rarefaction and viscous dissipation
Published in Numerical Heat Transfer, Part A: Applications, 2019
Figure 4 shows axial distributions of the pressure, streamwise velocity, density, and temperature for decreasing tube diameter. For a constant Reynolds number, if the tube diameter decreases, the velocity magnitude should be increased and the frictional force becomes large because of the presence of high velocity gradients. In this case, a large pressure difference is necessary to overcome the increased friction. This feature can be explained as follows for P/Pin at the centerline in Figure 4a. In small microtubes, increased pressure drops are observed in the flow direction. Figure 4b depicts streamwise velocities at the centerline. The velocity ratio u/Uin develops to about two for large microtubes with D-values of 10 and 5 μm, but it increases nonlinearly for smaller microtubes with D-values of 2 and 1 μm. Thus, flows in small-diameter microtubes are very different from those in large-diameter microtubes. Therefore, for small microtubes, the streamwise acceleration of compressible flow can be considered as one of the factors representing the size effect. The centerline densities observed for a decreasing tube diameter are plotted in Figure 4c, and Figure 4d shows the cross-sectional mean temperature in the streamwise direction. The meaningful reduction of density is higher for smaller diameters. Unlike incompressible flow, the density of compressible flow is very sensitive to pressure and temperature. According to the ideal gas law, the density is directly proportional to the pressure and inversely proportional to the temperature. At the exit x* = 0.4, we have ρ/ρin = 0.45 and Tm/Tin = 0.93. Thus, as the diameter decreases, the density reduction resulting from the increased pressure drop is more dominant than that associated with temperature changes. This result explains the velocity increase in the axial direction. Since the mass flow rate () is constant, naturally, the velocity increases with a decrease in the density in the axial direction. In Figure 4d, the theoretical temperature obtained from the energy conservation for incompressible flow is represented by the black line (obtained from the expression where and denote the surface area and perimeter of the microtube, respectively) for distinguishing the size effect. For a tube diameter of 10 μm, it agrees well with the theoretical temperature. However, as the diameter decreases, the temperature rise decreases. For the smallest diameter (1 μm), the outlet temperature is less than the inlet temperature, although heat transfer is from the wall to the fluid. This implies that the heat energy from the wall is used for changing the fluid state, which is not expected in incompressible flows.