Incompressible fluid flow

Example 1 Force Exerted on a Reducing Bend An incompressible fluid flows through a reducing elbow (Fig. 6-5) situated in a horizontal plane. The inlet velocity Vj is given and the pressures pi and measured. 

Example 3 Venturi Flowmeter An incompressible fluid flows through the venturi flowmeter in Fig. 6-7. An equation is needed to relate the flow rate Q to the pressure drop measured by the manometer. This problem can he solved using the mechanical energy balance. In a well-made venturi, viscous losses are neghgihle, the pressure drop is entirely the result of acceleration into the throat, and the flow rate predicted neglecting losses is quite accurate. The inlet area is A and the throat area is a. 

This example demonstrates the dimensioning of a duct with a frictional incompressible fluid flow. Now the Bernoulli equation can be written as... 

The steady, laminar, incompressible fluid flow in cyclone collectors is governed by the Navier-Stokes equations ... 

For steady, incompressible fluid flow in a cyclone separator, the governing Navier-Stokes equations of motion are given, in a Cartesian coordinate system, by ... 

The Navier-Stokes equations are the fundatnenta equations describing incompressible, fluid flow see Chapter 9. 

For an incompressible fluid flowing in a horizontal pipe of constant cross-section, in the absence of work being done by the fluid on the surroundings, the pressure change due to frictional effects is given by ... 

In our analysis, we discuss experimental results of heat transfer obtained by previous investigators and related to incompressible fluid flow in micro-channels of different geometry. The basic characteristics of experimental conditions are given in Table 4.1. The studies considered herein were selected to reveal the physical basis of scale effect on convective heat transfer and are confined mainly to consideration of laminar flows that are important for comparison with conventional theory. 

VAN Doormal, ). P., Raithby, G. D., Enhancement of the SIMPLE method for predicting incompressible fluid flows. Numerical Heat Transfer 7 (1984) 147-163. 

For a fan the changes in pressure and temperature are small enough that the incompressible fluid flow equations given for pumps may be used. In fact, for most gas systems, if the pressure drop is less than 40% of absolute upstream pressure the fluids can be treated as incompressible.30... 

Consider a section of uniform cylindrical pipe of length L and radius R, inclined upward at an angle 0 to the horizontal, as shown in Fig. 6-2. The steady-state energy balance (or Bernoulli equation) applied to an incompressible fluid flowing in a uniform pipe can be written... 

Flashing liquids escaping through holes and pipes require special consideration because two-phase flow conditions may be present. Several special cases need consideration.17 If the fluid path length of the release is short (through a hole in a thin-walled container), nonequilibrium conditions exist, and the liquid does not have time to flash within the hole the fluid flashes external to the hole. The equations describing incompressible fluid flow through holes apply (see section 4-2). 

An important application of Bernoulli s equation is in flow measurement, discussed in Chapter 8. When an incompressible fluid flows through a constriction such as the throat of the Venturi meter shown in Figure 8.5, by continuity the fluid velocity must increase and by Bernoulli s equation the pressure must fall. By measuring this change in pressure, the change in velocity can be determined and the volumetric flow rate calculated. 

An incompressible fluid flows upwards in steady state in a cylindrical pipe at an angle 8 with the horizontal. Assume that the head loss due to friction is negligible. 

When considering flow of a liquid in contact with a solid surface, a basic understanding of the hydrodynamic behavior at the interface is required. This begins with the Navier-Stokes equation for constant-viscosity, incompressible fluid flow, such that Sp/Sf = 0,... 

An incompressible fluid flows in a laminar steady fashion through a long pipe with a linear pressure gradient. Describe the velocity profile and determine the relationship for the Darcy-Weisbach friction factor. 

A useful discussion of incompressible fluid flow in pipes and the influence of surface roughness and friction factors on pumping is found in Perry s Chemical Engineer s Handbook (49). 

The dynamics of the incompressible fluid flow depend on small changes in the pressure through the flowfield. These changes are negligible compared to the absolute value of the thermodynamic pressure. The reference value can then be taken as some pressure at a fixed point and time in the flow. Changes in pressure result from fluid dynamic effects and an appropriate pressure scale is where Vmax is a measure of the maximum velocity in... 

An incompressible fluid flows into one end of an isothermal porous tube that is blocked on the far end (Fig. 4.31). The mass flux through the tube walls is proportional to the local pressure difference across the tube wall,... 

Example 1 Force Exerted on a Reducing Bend An incompressible fluid flows through a reducing elbow (Fig. 6-5) situated in a horizontal plane. The inlet velocity Vl is given and the pressures pl and p. are measured. Selecting the inlet and outlet surfaces 1 and 2 as shown, the continuity equation Eq. (6-9) can be used to find the exil velocity Vz = VjA/A. The mass flow rate is obtained by m = p V. A. ... 

Assuming that T(z, tf) = Tw, we can deal with the flow problem alone for tj < t < tc. Referring to Fig. 13.45, as long as the preform radius is less than Ro, we can treat the problem as an isothermal radial flow of an incompressible fluid flowing between two disks that approach each other at a constant rate h. Recapturing the results for the velocity field, pressure distribution, and plunger force needed to squeeze an isothermal Power Law fluid at a constant slow or moderate squeeze rate, we have... 

From the conservation of mass for an incompressible fluid flowing through the orifice we find that... 

Chang, Y.C., Hou, T.Y., Merriman, B., and Osher, S. (1996) A level set formulation of Eulerian interface capturing methods for incompressible fluid flows, Journal of Computational Physics, Vol. 124, pp. 449-464. 

Will the kinetic energy per unit mass of an incompressible fluid flowing in a pipe increase, decrease, or remain the same if the pipe diameter is increased at some place in the line ... 

Assume there is an incompressible fluid flow with a constant density p the above equation can then be simplified as a very important special form of the continuity equation... 

Amsden AA, Harlow FH (1970) A Simplified MAC Technique for Incompressible Fluid Flow Calculations. J Comput Phys 6 322-325... 

Chang YC, Hou TY, Merriman B, Osher S (1996) A Level Set Formulation of Eulerian Interface Capturing Methods for Incompressible Fluid Flows. J Comput Phys 124 449-464. 

Demirdzic I, Lilek Z, Peric M (1993) A Collocated Finite Volume Method for Predicting Flows at all Speeds. Int J Numer Methods Fluids 16 1029-1050 Deville MO, Fischer PF, Mund EH (2002) High-Order Methods for Incompressible Fluid Flow. Cambridge University Press, Cambridge... 

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