Querschnittsfluss

Querschnittsfluss is the volumetric flow rate through a defined cross-section of a fluid system, such as a pipe, duct, or channel. It is a fundamental quantity in fluid dynamics and hydrology and is usually denoted by Q. The SI unit is cubic meters per second (m^3/s).

Mathematically, Q is given by the integral Q = ∫A v · n dA, where A is the cross-sectional area, v is the local velocity field, and n is the unit normal vector to the cross-section. In many practical cases the velocity distribution is approximately uniform across A, yielding the simplified expression Q = v̄ A, with v̄ the average velocity normal to the cross-section.

In incompressible, steady flow, the principle of continuity implies that Q remains constant along a streamline or through successive cross-sections of a closed conduit, provided there are no sources or sinks. When a conduit changes cross-sectional area, velocity adjusts so that the same Q passes through, even though the mean velocity and the shape of the velocity profile may change.

Measurement and computation: Q can be measured directly with flow meters, such as magnetic, ultrasonic, or turbine meters, or computed numerically in computational fluid dynamics. In open-channel flow, Q is obtained by integrating the velocity distribution over the cross-sectional area of the water surface and cross-section.

Applications and related concepts: Querschnittsfluss is essential in designing piping networks, ventilation systems, irrigation channels, and in hydrological assessments. Related terms include Durchfluss, Durchflussrate, and the continuity equation.