Kinetic energy correction factor

Therefore, a kinetic energy correction factor, a, can be defined as the ratio of the true rate of kinetic energy transport relative to that which would occur if the fluid velocity is everywhere equal to the average (plug flow) velocity, e.g.,... 

The Bernoulli equation should therefore include this kinetic energy correction factor, i.e.,... 

Example 5-2 Kinetic Energy Correction Factor for Laminar Flow of a Newtonian Fluid. We will show later that the velocity profile for the laminar flow of a Newtonian fluid in fully developed flow in a circular tube is parabolic. Because the velocity is zero at the wall of the tube and maximum in the center, the equation for the profile is... 

This can be used to calculate the kinetic energy correction factor from Eq. (5-38) as follows. First we must calculate the average velocity, V, using... 

Evaluate the kinetic energy correction factor a in Bernoulli s equation for turbulent flow assuming that the 1/7 power law velocity profile [Eq. (6-36)] is valid. Repeat this for laminar flow of a Newtonian fluid in a tube, for which the velocity profile is parabolic. 

The a s are the kinetic energy correction factors at the upstream and downstream points (recall that a = 2 for laminar flow and a = 1 for turbulent flow for a Newtonian fluid). 

Fig. 9. Dependence of kinetic-energy correction factor upon flow-behavior index.

It was noted that the velocity in a channel approaching a weir might be so badly distributed as to require a value of 1.3 to 2.2 for the kinetic energy correction factor. In unobstructed uniform channels, however, the velocity distribution not only is more uniform but is readily amenable to theoretical analysis. Vanonil has demonstrated that the Prandtl universal logarithmic velocity distribution law for pipes also applies to a two-dimensional open channel, i.e., one that is infinitely wide. This equation may be written... 

In the MEB equation, kinetic energy losses can be calculated easily provided that the kinetic energy correction factor a can be determined. In turbulent flow, often, the value of a = 2 is used in the MEB equation. When the flow is laminar and the fluid is Newtonian, the value of a = 1 is used. Osorio and Steffe (1984) showed that for fluids that follow the Herschel-Bulkley model, the value of a in laminar flow depends on both the flow behavior index ( ) and the dimensionless yield stress ( o) defined above. They developed an analytical expression and also presented their results in graphical form for a as a function of the flow behavior index ( ) and the dimensionless yield stress ( o)- When possible, the values presented by Osorio and Steffe (1984) should be used. For FCOJ samples that do not exhibit yield stress and are mildly shear-thinning, it seems reasonable to use a value of a = 1. 

Kinetic-energy correction factor. It is convenient to eliminate the integral of Eq. 

For incompressible fluids, the Bernoulli equation is corrected for friction by adding a term to the right-hand side of Eq. (4.25). Thus, after introducing the kinetic-energy correction factors and Kj, Eq. (4.25) becomes... 

A liquid is flowing in steady flow through a 75-mm pipe. The local velocity varies with distance from the pipe axis as shown in Table 4.1. Calculate (n) average velocity K (b) kinetic-energy correction factor a, and (c) momentum correction factor / ,... 

AVERAGE VELOCITY, KINETIC-ENERGY FACTOR, AND MOMENTUM CORRECTION FACTOR FOR LAMINAR FLOW OF NEWTONIAN FLUIDS. Exact formulas for the average velocity V, the kinetic-energy correction factor a, and the momentum correction factor P are readily calculated from the defining equations in Chap. 4 and the velocity distribution shown in Eq. (5.11). 

Kinetic-energy correction factor. The kinetic-energy factor a is calculated from Eq. (4.29X using Eqs. (5.8) for dS, (5,11) for u, and (5.14) for V. The final result is a = 2.0. The proper term for kinetic energy in the Bernoulli equation for laminar flow is therefore V /gc-... 

The kinetic-energy correction factor may be important in applying Bernoulli s theorem between stations when one is in laminar flow and the other in turbulent flow. Also, factors a and p are of some importance in certain types of compact heat-exchange equipment, where there are many changes in size of the fluid channel and where the tubes or heat-transfer surfaces themselves are short. In most practical situations both are taken as unity in turbulent flow. 

Kinetic-energy correction factor a , at station a a, at station b ttj,., at station b also angle between absolute and peripheral velocities in pump impeller oci, at suction aj, at discharge Vane angle in pump impeller at suction / 2, at discharge also ratio, diameter of orifice or venturi throat to diameter of pipe Ratio of specific heats, Cp/c ... 

In order to obtain the kinetic energy correction factor, a, for insertion in the mechanical energy balance, it is necessary to evaluate the average kinetic energy per xmit mass in terms of the average velocity of flow. The calculation procedme is exactly similar to that used for Newtonian fluids, (e g. see [Coulson and Richardson, 1999]). 

The asymptotic kinetic energy correction factor K. defined as ... 

Values of the momentum and kinetic-energy correction factors depend on the details of the velocity distribution for a particular flow. For flow in circular pipes the following values are obtained ... 

Flow Between Parallel Plates and Kinetic-Energy Correction Factor. The equa-... 

---