Kinetic Energy Correction Factor

We have assumed in the derivation of Bernoulli equation that the velocity at the end sections (1) and (2) is uniform. But in a practical situation this may not be the case and the velocity can very across the cross section. A remedy is to use a correction factor for the kinetic energy term in the equation. If $ \overline{V}$is the average velocity at an end section then we can write for energy,

$\displaystyle \int_A {V^2 \over 2} \rho V.dA~=~\alpha
 \dot{m} {\overline{V}^2 \over 2}$ (3.75)

After simplification we find that

$\displaystyle \alpha~=~{1 \over A} ~\int_A ~\left( u \over \overline{V}
 \right)^3~ dA$ (3.76)

Consequently, Eqn.3.70 (Low Speed Application) is written as

$\displaystyle \left(~{p \over \gamma}+~z~+~\alpha_1~{V^2
 \over {2g}} \right)_1...
 \over {2g}} \right)_2~+~h_{friction}~-~h_{pump}~+~h_{turbine}$ (3.77)

where $ \alpha$ is the Kinetic Energy Factor. Its value for a fully developed laminar pipe flow is around 2, whereas for a turbulent pipe flow it is between 1.04 to 1.11. It is usual to take it is 1 for a turbulent flow. It should not be neglected for a laminar flow.

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney