Kinetic Energy Correction Factor for Laminar Flow through Circular Pipe

Kinetic energy correction factor is defined as the ratio of actual kinetic energy of fluid to the kinetic energy calculated by assuming the fluid to be incompressible and inviscid. It is denoted by Ck.

For laminar flow through a circular pipe, the value of kinetic energy correction factor is approximately equal to 2.0.

Explanation

The kinetic energy correction factor takes into account the effect of viscosity on the flow of fluid. In laminar flow, the fluid particles move in a smooth and orderly manner, with no turbulence or mixing. Therefore, the effect of viscosity is more pronounced in laminar flow than in turbulent flow.

For a circular pipe, the actual kinetic energy of fluid is given by:

E = (π/8)ρQ²D²

where ρ is the density of fluid, Q is the volumetric flow rate, and D is the diameter of the pipe.

The kinetic energy calculated by assuming the fluid to be incompressible and inviscid is given by:

E0 = (π/8)ρQ²D²/(1 + 3λ/2D)

where λ is the viscosity of fluid.

Therefore, the kinetic energy correction factor is given by:

Ck = E/E0 = 1 + 3λ/2D

For laminar flow through a circular pipe, the value of λ/D is small, and can be approximated to zero. Therefore, the value of kinetic energy correction factor is approximately equal to 2.0.

Conclusion

In conclusion, the value of kinetic energy correction factor for laminar flow through a circular pipe is approximately equal to 2.0. This value takes into account the effect of viscosity on the flow of fluid, and is important in the design and analysis of fluid systems.