Mass is conserved: A1V1=A2V2 for incompressible flow.
Conservation of mass: ṁ=ρAV is the same at every section in steady flow; for incompressible flow Q=AV is constant. A smaller area means higher velocity. For control volumes: ∑ṁ_in-∑ṁ_out=dm/dt. Differential form ∇·V=0 for incompressible flow.
Water in a 100 mm pipe at 2 m/s speeds to 8 m/s in a 50 mm nozzle.
The continuity equation links velocity and area in a pipe or duct, so it determines how flow speeds up or slows down along a system.
Mass is conserved: A1V1=A2V2 for incompressible flow.
The continuity equation links velocity and area in a pipe or duct, so it determines how flow speeds up or slows down along a system.
The mass flow rate is the same at every section, so for incompressible flow the velocity increases when the area decreases.
For steady, incompressible flow in a single stream, and for compressible flows the density must be included.
Typical applications include finding the velocity in a narrow section of a pipe from the wider section, sizing a duct to keep air velocity within limits and calculating the water speed in a garden hose with a nozzle.
Study "Fluid kinematics" first (topic 51 of 105 in Thermodynamics & Fluids). It covers the groundwork this topic builds on.
Volume flow rate Q m³/s. Nozzle speed-up. Branches add flows.
Water in a 100 mm pipe at 2 m/s speeds to 8 m/s in a 50 mm nozzle.
The next topic is "Bernoulli equation", which builds directly on this one.
It is classed as Intermediate in Thermodynamics & Fluids (topic 52 of 105). It is an intermediate topic. Work through the beginner topics in Thermodynamics & Fluids first.
Want to practise? Open the interactive course for quick checks, quizzes, simulations and progress tracking.