Impact pressure coefficient and object mobilization length in mass flows

As the impact force of a flow overcomes the frictional resistance of an object, the object moves as long as the pressure exerted by the flow is greater than its shear resistance. With this concept, here, we develop simple analytical models for the mechanical description of the coefficient of impact pressure Cp0 and the mobilization length L when a mass flow impacts a movable object. We invented the obstacle mobilization number Cp0, a dimensionless number, which is expressed as the ratio of the obstacle shear resistance to the kinetic energy of the flow, per unit length. We also relate it to the obstacle Froude number Fr0. When the object moves through the length L against the basal friction, after consuming its kinetic energy, the object eventually stops. This balance between the kinetic energy and friction yields an analytical model for the mobilization length of the object. Equivalently, if the mobilization length is known, the impact velocity can be calculated. This is very important in estimating the flow velocity of any large-scale natural mass flows. Our model predicts that Cp0 decreases strongly to weakly non-linearly with the impact velocity, density ratio between the granular particle and the mobile object, and the area ratio between the grain covered area of the object and its base. Moreover, Cp0 increases linearly with the basal friction coefficient. However, the dynamic response of Cp0 to the shape of the object may vary immensely between objects of different shapes. Our model also predicts that the mobilization length L of the mobile object varies with the square of the impact velocity of flowing mass, but decreases with basal friction of the obstacle and the component of gravitational acceleration in the direction normal to the flow depth. We conduct several laboratory chute experiments with different native Nepalese complex fruit seeds and food grains to validate the physical significance and scope of Cp0 and L. Our simple analytical models very well describe the coefficient of impact pressure and the mobilization length of the mobile object impacted by the laboratory granular flows. We discuss the applicability of Cp0 and L to real flow situations in designing protective civil defense structures as well as mitigating from natural disasters, and industrial transports of complex granular flows.