with the same stream power, as they are losing the same amount of energy but in the narrow river it is concentrated into a smaller area. Critical Unit Stream Power Critical unit stream power is the amount of stream power needed to displace a grain of a specific size, it is given by the equation:where τ0 is the critical shear stress of the grain size that will be moved which can be found in the literature or experimentally determined while v0 is the critical mobilization speed. Relationships to other variables Size of displaced sediment Critical stream power can be used to determine the stream competency of a river, which is a measure to determine the largest grain size that will be moved by a river. In river's with large sediment the relationship between critical unit stream power and sediment diameter displaced can be reduce to:While in intermediate-sized rivers the relationship was found to follow: Shear stress Shear stress is another variable used in erosion and sediment transport models representing the force applied on a surface by a perpendicular force, and can be calculated using the following formulaWhere is the shear stress, S is the slope of the water, ρ is the density of water (1000 kg/m3), g is acceleration due to gravity (9.8 m/s2). Shear stress can be used to compute the unit stream power using the formulaWhere V is the velocity of the water in the stream. Applications Landscape evolution Stream power is used extensively in models of landscape evolution and river incision. Unit stream power is often used for this, because simple models use and evolve a 1-dimensional downstream profile of the river channel. It is also used with relation to river channel migration, and in some cases is applied to sediment transport. Predicting flood plain formation By plotting stream power along the length of a river course as a second-order exponential curve, you are able to identify areas where flood plains may form and why they will form there. Sensitivity to erosion Stream power has also been used as a criterion to determine whether a river is in a state of reshaping itself or whether it is stable. A value of unit stream power between 30 and 35 W m−2 in which this transition occurs has been found by multiple studies. Another technique gaining popularity is using a gradient of stream power by comparing the unit stream