KINETIC ENERGY CORRECTION FACTOR, MOMENTUM CORRECTION FECTOR

1.KINETIC ENERGY CORRECTION FACTOR
● In Bernoulli's equation, the velocity head computed on the basis of the assumption that velocity is uniform over the entire cross section of the stream tube. But in the case of flow of real fluids, the velocity distribution across any cross sectional area of the flow passage is not uniform.
● So, the actual kinetic energy possessed by the fluid is different from that computed by using the mean velocity.
● To obtain actual kinetic energy, kinetic correction factor is multiplied to kinetic energy obtained through mean velocity.
● Consider fluid is flowing in a circular pipe of area A. Taken an elementary strip of area dA at which velocity of flow is 'v' at a cross section.


● For ideal flow profile , a=1.0
● For turbulent flow in circular pipe a=1.03 to 1.06.
● For laminar flow in circular pipe a=2 and parallel plate a=1.543.
● Value of a for laminar flow is greater than for the turbulent flow because in laminar flow velocity gradient across the section is greater than the turbulent flow.
●Accordingly the modified Bernoulli's equation between any two section is:


2.MOMENTUM CORRECTION FACTOR
● A similar parameter momentum correction factor is defined in momentum equations as:

3. APPLICATION OF BERNOULLI'S EQUATION
1. Venturimeter
2. Orifice Meter
3. Nozzle Meter
4. Pitot Tube
5. Prandtl Tube or Pitot Static Tube

VENTURIMETER:

* It is a device used for measuring the rate of flow of fluid through pipe.
*Principle: By reducing the cross sectional area of the flow passage, a pressure difference enables the determination of discharge through the pipe. The geometry of Venturimeter is as shown in figure.
* flat at the late and short A1 and A2 with the cross-sectional areas, P1 and P2 be the pressures, V1 and V2 are velocities respectively. Then why applying Bernoulli's equation between section 1 and 2,
we get, be the
* in general, for Fluids of low viscosity a value of 0.98 is adopted for Cd.
* in Venturi metre as bi have gradual contraction and gradual expansion, there is no flow separation and hence, A2 can be taken as complete area of throat.
* Tenu convergent conflow is accelerating which may be allowed to take place rapidly in smaller length. Violin divergent cone retardation of flow occurs. If retardation of flow takes place in small length it will lead to flow separation and energy loss.
* Since separation of lawmakers in the divergent cone of Venturi metre, this person is not used for discharge measurement.
* Since, the cross sectional area of throat is smaller than that of inlet section, the velocity of flow at the throat is Greater, thus, the pressure is reduced at throat.
* if cross sectional area of throat is so much reduce that pressure drop below vapour pressure of flowing fluid, Cavitation may occur. Hence, to avoid the phenomena of Cavitation the diameter of throat can be reduced only up to certain Limited value.

● ORIFICE METER
* this device is used for measuring discharge through pipes which works on the same principal as Venturi metre.
* However orificemeter is a cheaper arrangement.
* As such where the space is limited, the orifice metre may be used for measurement of discharge through pipes.
* An orifice metre consists of a flat circular plate with a circular hole called orifice coma which is concentric with the pipe axis.
* the diameter of orifice may vary from 0.2 to 0.85 times the pipe diameter but generally kept at 0.5 times the pipe diameter .
* Let P1, P2 and V1, V2 the pressure and velocity is respectively sections 1 and 2. Then why applying Bernoulli's equation,

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