Final answer:
The question pertains to the physics concept of a 2-dimensional velocity field in fluid dynamics, where velocity vectors are used to illustrate fluid flow and mass flow rate is an important quantity calculated using the relationship between flow rate and velocity.
Step-by-step explanation:
When we consider a 2-dimensional flow with a velocity field that can be described by the expressions provided, we are discussing a concept from the field of Physics, more specifically fluid dynamics. For average velocity in two dimensions, we use the vector equivalent of the one-dimensional average velocity.
The velocity field is characterized by velocities depicted as vectors indicating both magnitude and direction (speed and vector direction) on a coordinate system. Analytical methods allow us to find the relationships between the magnitude of velocity (v) and its components (vx and vy) along the x- and y-axes of an appropriately chosen coordinate system. This is particularly important when dealing with physical phenomena like airflow patterns in meteorology or water flow in pipes.
In fluid dynamics, when considering incompressible fluids, we use the concept that the flow rate (Q) is equal to the cross-sectional area (A) times the average velocity (U). This relationship is crucial for applications such as calculating the mass flow rate, which must be conserved across various points in a system, leading to different velocities at different cross-sectional areas of flow paths, as described by Bernoulli's equation.