Izbash formula

The Izbash formula is a mathematical expression used to calculate the stability of armourstone in flowing water environments.

The former is more appropriate for fine-grained materials like sand and gravel, whereas the Izbash formula is tailored for larger stone sizes.

Its general expression is as follows:[1] Here, the variables represent: The coefficient 1.7 is an experimental constant determined by Izbash, encapsulating effects such as friction, inertia, and the turbulence of the current.

Hence, the application of this coefficient is limited to conditions where turbulence is predominantly induced by the roughness of the construction materials in water.

Analysing the moment equilibrium around point A results in FF being disregarded due to its zero arm length.

Balancing the active forces against the passive ones yields the critical flow velocity equation: K is an empirical coefficient calibrated through experimental observations, and has been found to be around 1.7.

[2] Consider determining the requisite stone size to protect the base of a channel with a depth of 1 m and an average flow rate of 2 m/s.

The application of the formula necessitates the measurement of velocity in proximity to the stone, a task that can be challenging, particularly in fine-grained soils and at significant water depths.

[3] Recognising the prevalent usage of the coefficient 0.7, Krystian Pilarczyk refined the formula in 1985 for enhanced specificity.

Displayed is the velocity after subtracting the average speed, i.e., the u and v components (for further explanation, see the main article on Turbulence modelling).

In the wake of a vessel in a narrow channel, a strong return flow with increased turbulence is observed, where r is typically around 0.2.