Fluid flow average velocity

For steady-state laminar flow of any time-independent viscous fluid, at average velocity V in a pipe of diameter D, the Rabinowitsch-Mooney relations give a general relationship for the shear rate at the pipe wall. 

First, consider the flow of an incompressible fluid in a straight pipe. The pressure drop is a function of the density and viscosity of the fluid, the average velocity of the fluid, and the diameter and length of the pipe. The relationship is usually expressed by means of a friction factor defined as in Eq. (1) ... 

In faa, some flow-measuring devices make use of Equation (8.12) to determine the volume flow rate of a fluid by first measuring the fluid s average velocity and the cross-sectional area of the flow. Finally, note that in Chapter 9 we will explain another closely defined variable, mass flow rate of a flowing material, which provides a measure of time rate of mass flow through pipes or other carrying conduits. 

The presence of the film between the dispersed plug and the channel wall offers multiple advantages such as prevention from cross contamination between the segments in biological devices, and enhancement of the heat and mass transfer in chemical engineering processes. Film thickness can be affected by different parameters such as fluid properties, average velocity, flow rate ratio, and channel size. 

Although they are increasingly popular, computational fluid dynamic (CFD) calculations are notoriously difficult to validate Model equations may be available to the user, but the source code is typically proprietary, experimental data for comparison may be impossible to obtain, and the sheer volume of data available from the simulations makes complete and meaningful validations extremely difficult. Velocity measurements are difficult. Pressure drop measurements are easy but insensitive to the details of the flow. The RTD is a more sensitive test, but it is not unique since the RTD is derived from a flow-averaged velocity profile... 

For a single fluid flowing through a section of reservoir rock, Darcy showed that the superficial velocity of the fluid (u) is proportional to the pressure drop applied (the hydrodynamic pressure gradient), and inversely proportional to the viscosity of the fluid. The constant of proportionality is called the absolute permeability which is a rock property, and is dependent upon the pore size distribution. The superficial velocity is the average flowrate... 

The Reynolds number for flow in a tube is defined by dvpirj, where d is the diameter of the tube, V is the average velocity of the fluid along the tube, p is the density of the fluid, and rj is its dynamic viscosity. At flow velocities corresponding with values of the Reynolds number of greater than 2000, turbulence is encountered. 

A separate equation is obtained for each component i Consider the important case of steady-state flow of a single fluid through the pipe section of Figure 21b, where the flow is taken to be perpendicular to the cross sections and Making use of the concept of average velocity ... 

Measurement by Thermal Effects. When a fine wire heated electrically is exposed to a flowing gas, it is cooled and its resistance is changed. The hot-wire anemometer makes use of this principle to measure both the average velocity and the turbulent fluctuations in the flowing stream. The fluid velocity, L, is related to the current, /, and the resistances, R, of the wire at wire, and gas, g, temperatures via... 

Laminar and Turbulent Flow, Reynolds Number These terms refer to two distinct types of flow. In laminar flow, there are smooth streamlines and the fuiid velocity components vary smoothly with position, and with time if the flow is unsteady. The flow described in reference to Fig. 6-1 is laminar. In turbulent flow, there are no smooth streamlines, and the velocity shows chaotic fluctuations in time and space. Velocities in turbulent flow may be reported as the sum of a time-averaged velocity and a velocity fluctuation from the average. For any given flow geometry, a dimensionless Reynolds number may be defined for a Newtonian fluid as Re = LU p/ I where L is a characteristic length. Below a critical value of Re the flow is laminar, while above the critical value a transition to turbulent flow occurs. The geometry-dependent critical Reynolds number is determined experimentally. 

Here g is the gravity vector and tu is the force per unit area exerted by the surroundings on the fluid in the control volume. The integrand of the area integr on the left-hand side of Eq. (6-10) is nonzero only on the entrance and exit portions of the control volume boundary. For the special case of steady flow at a mass flow rate m through a control volume fixed in space with one inlet and one outlet, (Fig. 6-4) with the inlet and outlet velocity vectors perpendicular to planar inlet and outlet surfaces, giving average velocity vectors Vi and V9, the momentum equation becomes... 

ASpGr = Difference in specific gravity of the particle and the surrounding fluid tyvg = Average residence time based on liquid flow rate and vessel volume, min tmjp = Minimum residence time to allow particles to settle based on Stokes Law, min u = Relative velocity between particle and main body of fluid, ft/sec... 

In turbulent flow there is a complex interconnected series of circulating or eddy currents in the fluid, generally increasing in scale and intensity with increase of distance from any boundary surface. If, for steady-state turbulent flow, the velocity is measured at any fixed point in the fluid, both its magnitude and direction will be found to vary in a random manner with time. This is because a random velocity component, attributable to the circulation of the fluid in the eddies, is superimposed on the steady state mean velocity. No net motion arises from the eddies and therefore their time average in any direction must be zero. The instantaneous magnitude and direction of velocity at any point is therefore the vector sum of the steady and fluctuating components. 

A liquid is pumped in streamline flow through a pipe of diameter d. At what distance from the centre of the pipe will the fluid be flowing at the average velocity ... 

The density profile for the micropore fluid was determined as In the equilibrium simulations. In a similar way the flow velocity profile for both systems was determined by dividing the liquid slab Into ten slices and calculating the average velocity of the particles In each slice. The velocity profile for the bulk system must be linear as macroscopic fluid mechanics predict. 

The first example pertains to forced convection in pipe flow. It is found that the rate of heat transfer between the pipe wall and a fluid flowing (turbulent flow) through the pipe depends on the following factors the average fluid velocity (u) the pipe diameter (d) the... 

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