How the loss coefficient K can be calculated for sudden contraction?

The loss coefficient ( K ) for a sudden contraction can be calculated using the formula:

[ K = \left(1 - \frac{A_2}{A_1}\right)^2 ]

where ( A_1 ) is the cross-sectional area of the larger duct and ( A_2 ) is the cross-sectional area of the smaller duct. This formula assumes that the flow is incompressible and that the contraction is sudden, leading to turbulence and energy loss. The resulting ( K ) value represents the energy loss due to the abrupt change in flow area.