Base unit (measurement) aspects of the world, such as time, distance, velocity, mass, temperature, energy, and weight, and "units" are used to describe their magnitude or quantity. Many of these quantities are related to each other by various physical laws, and as a result the units of a quantities can be generally be expressed as a product of powers of other units; for example, momentum is mass multiplied by velocity, while velocity is measured in distance divided by time. These relationships are discussed in dimensional analysis. Those that can be expressed in this fashion in terms of the base units are called .
Velocity gradient analysis, the dimensions of velocity gradient can be determined. The dimensions of velocity are formula_4 , and the dimensions of distance are formula_5. Since the velocity gradient can be expressed as formula_6. Therefore, the velocity gradient has the same dimensions as this ratio, i.e. formula_7. In 3 dimensions, the gradient, formula_8 , of the velocity formula_9 is a second-order tensor which can be expressed as the matrix L: formula_11 can be decomposed into the sum of a symmetric matrix formula_12 and a skew-symmetric matrix formula_13 as follows formula_12 is called the strain rate tensor and describes the rate of stretching