Equation of Continuity

Volume flow rate is the volume of fluid flowing through a point in an area per unit time. It is calculated by multiplying the cross-sectional area of the pipe by the velocity of the fluid. This relationship shows that flow rate depends on both the size of the conduit and how fast the fluid moves through it.

When a pipe's cross-sectional area decreases, the fluid velocity must increase to maintain continuity of flow. Since the same amount of incompressible fluid must pass through any point in the pipe per unit time, a smaller area requires higher velocity to conserve the volume flow rate.

The equation of continuity states that the volume flow rate entering a pipe equals the volume flow rate leaving it. For incompressible fluids, density cancels out, so the product of cross-sectional area and velocity remains constant throughout the pipe, ensuring mass conservation.

Mass flow rate equals density multiplied by volume flow rate. It represents the mass of fluid passing through a point per unit time. For steady flow through a pipe with no sources or sinks, the mass flowing in must equal the mass flowing out.

For steady flow, the velocity and density of the fluid at any point must remain constant over time. Additionally, the pipe must have no sources or sinks that add or remove fluid, ensuring that mass entering the pipe equals mass leaving it at all times.

Liquids are essentially incompressible, so their density remains constant, making the equation of continuity universally valid for all liquid flow. Gases are compressible, so the equation must be applied with caution when gases undergo compression or expansion, as density changes affect flow relationships significantly.

The equation of continuity ensures mass conservation in steady flow by maintaining constant volume flow rate through varying pipe sections. This principle connects to energy conservation and bernoulli equation principles, where changes in velocity and pressure are governed by both mass continuity and energy conservation in fluid systems.