The continuity equation asserts that the mass flow rate must remain constant for a steady flow of an incompressible fluid within a confined system. This principle applies to systems where fluid passes through varying cross-sectional areas, such as nozzles, syringes, and pipes.
The mass flow rate is expressed as:

A function is continuous at a point a if three conditions are met: the function is defined at a, the limit of the function as x approaches a exists, and this limit equals the function’s value. Mathematically, this is written asThis definition ensures the graph of the function does not exhibit any breaks, holes, or jumps at that point. Discontinuities occur when any of these conditions fail. A removable discontinuity exists when the two-sided limit exists but the function is either...

Tumor progression is a phenomenon where the pre-formed tumor acquires successive mutations to become clinically more aggressive and malignant. In the 1950s, Foulds first described the stepwise progression of cancer cells through successive stages.
Colon cancer is one of the best-documented examples of tumor progression. Early mutation in the APC gene in colon cells causes a small growth on the colon wall called a polyp. With time, this polyp grows into a benign, pre-cancerous tumor. Further...

Continuing care describes the variety of health, personal, and social services provided over a prolonged period. The need for continuing care is increasing because people are living longer. Many people do not have families or others to care for them. Continuing care is mainly for patients who are disabled, functionally dependent, or suffering from a terminal disease. It is available within institutional settings or in homes. Examples include nursing centers or facilities, assisted living,...

The total amount of current flowing per unit cross-sectional area is called the current density. Hence, the current passing through a cross-sectional area can be written as the surface integral of the current density.

Fluid motion is represented by either velocity vectors or streamlines. The volume of a fluid flowing past a given location through an area during a period of time is called the flow rate Q, or more precisely, the volume flow rate. Flow rate and velocity are related—for instance, a river has a greater flow rate if the velocity of the water in it is greater. However, the flow rate also depends on the size and shape of the river. The relationship between flow rate (Q) and average speed (v)...