Momentum balance pdf

Then when we make a momentum balance over a thin cylindrical shell of liquid, we arrive at the following differential equation: This differs from Eq. Integration of Eq. That is,. When we solve this equation for C 1 and substitute it into Eq. The only difference between this equation and Eq. The advantage of this is that we know the geometrical significance of. Integration of this first-order separable differential equation then gives.

We now evaluate the two constants of integration, and C 2 by using the no-slip condition on each solid boundary:.

Substitution of these boundary conditions into Eq. From these the two integration constants and C 2 are found to be. These expressions can be inserted into Eqs. Note that when the annulus becomes very thin i. Once we have the momentum-flux and velocity distributions, it is straightforward to get other results of interest:. The equations derived above are valid only for laminar flow. The fluid flow rates are adjusted so that the slit is half filled with fluid I the more dense phase and half filled with fluid II the less dense phase.

The fluids are flowing sufficiently slowly that no instabilities occur-that is, that the interface remains exactly planar. It is desired to find the momentum-flux and velocity distributions. A differential momentum balance leads to the following differential equation for the momentum flux assume that no change of velocity profile at z direction :. This equation is obtained for both phase I and phase II.

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Did you find this document useful? Is this content inappropriate? Report this Document. The decreased velocity in the wake is sometimes referred to as the momentum defect. This momentum defect will be plot by plotting vs.

The drag is related to the integral of this quantity over the outgoing control surface. At constant wind tunnel speed the flow is a steady state flow.

Using the control volume shown in Figure 9. Static pressure is assumed to be constant throughout the constant cross-section test section of the wind tunnel rand is measured at the beginning of the test section. The pressure measuring device is referenced to the static pressure in the test section, the pressure sensed by the total pressure tap referenced to the static pressure is the dynamic head, [5] And the ratio, can be easily evaluated directly from measured data.

The experimental apparatus was set up as shown in Figure 8. The diameter of the circular cylinder was measured and recorded. The rack of 18 total pressure devices were secured behind the specimen. The wind tunnel was activated and pressure readings were recorded from the pressure devices as well as the manometer, which measured the pressure in inches of water. A separate mobile probe was used to measure the undisturbed flow, this reading was also recorded.

Steps 4 and 5 were repeated at a reduced air speed. Table 5. The area between the experimental data and velocity is shown. The data is then interpolated to the velocity ratio limit. The distance between each pitot was determined to be 0. This scale of measure was used to further accurately interpolate the data. This plot is shown below as Figure 6. The area between the experimental data curve and a velocity ratio of one is determined. Figure 5. The function is then evaluated over the desire range, The region between the two lines is then computed.

The interpolated experimental data is shown in Figure 5. The coefficient of drag was then determined for the trail using equation [4], 5. The error bars for this error are displayed bellowed as Figure 5. DOI: Spedding , E. Donnelly Published 1 November Materials Science International Communications in Heat and Mass Transfer Abstract Empirical correlations were tested against reliable two phase pipe flow data for the prediction of pressure drop.

Correlations are recommended for the prediction with stratified and annular type flows. When these correlations were adapted to three phase gas—water—oil pipe flow in general they predicted for intermittent slug type flows. Momentum balance models could not be successfully adapted to the prediction of pipe three phase pressure drop.

View via Publisher. Save to Library Save. Create Alert Alert. Share This Paper. Results Citations. Figures from this paper. Citation Type. Has PDF. Publication Type. More Filters. Investigation of pressure drop in horizontal pipes with different diameters. Abstract The pressure drop has a significant importance in multiphase flow systems.

In this paper, the effect of the volumetric quality and mixture velocity on pressure drop of gas-liquid flow in … Expand. View 1 excerpt, cites results. Numerical investigation of gas-liquid two-phase flow in horizontal pipe with orifice plate.

Abstract Gas-liquid two-phase flow in horizontal or vertical pipeline significantly impacts on the transportation process. In fact, in the pipeline for regulating the flow flux or pressure, orifice … Expand.