Fluid flow 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.,... 

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... 

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). 

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. 

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). 

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. 

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]). 

Water is pumped from a large reservoir to a point 65 ft higher than the reservoir. How many feet of head must be added by the pump if 8000 lb,yh flows through a 6 in. pipe and the frictional head loss is 2 ft The density of the fluid is 62.4 Ib ft and the pump efficiency is 60%. Assume the kinetic energy correction factor equals 1. 

For steady flow in a pipe or tube the kinetic energy term can be written as m2/(2 a) where u is the volumetric average velocity in the pipe or tube and a is a dimensionless correction factor which accounts for the velocity distribution across the pipe or tube. Fluids that are treated as compressible are almost always in turbulent flow and a is approximately 1 for turbulent flow. Thus for a compressible fluid flowing in a pipe or tube, equation 6.4 can be written as... 

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