The study attempts to develop a theory for the penetration of a wide range of solid materials by continuous high-velocity water jets. The theory is based on a control volume analysis to determine the hydrodynamic forces acting on the solid boundaries of the cutting slot. A Bingham model is used to describe the time-dependent stress-strain relationship of the solid material. The coupled fluid-solid mechanics equations are simplified to yield a closed-form solution in the form of a nondimensional cutting equation
$zdn=1−σcρV122Cf√π$
$[1−e−(2Cf/√π)·(ρV1/η)·(V1/u)]$
which satisfies all the limiting conditions of practical cutting applications. Published experimental results from cutting tests with a wide range of fibrous, granular and crystalline material are used to obtain mean values of the friction (Cf) and damping coefficients (η) which are used with the compressive yield strength (σc) to characterize different materials. The theory presents a basis for developing more exact cutting equations by choosing the optimum rheological model for a particular material.
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