8.4 Fluids and Conservation Laws

Describe the flow of an incompressible fluid through a cross-sectional area by using mass conservation.

• A difference in pressure between two locations causes a fluid to flow.
  • i. The rate at which matter enters a fluid-filled tube open at both ends must equal the rate at which matter exits the tube.
  • ii. The rate at which matter flows into a location is proportional to the crosssectional area of the flow and the speed at which the fluid flows. Derived equation: V =Avt
• The continuity equation for fluid flow describes conservation of mass flow rate in incompressible fluids. Relevant equation: Av11 =Av22 TOPIC 8.4 Fluids and Conservation Laws

Describe the flow of a fluid as a result of a difference in energy between two locations within the fluid– Earth system.

• A difference in gravitational potential energies between two locations in a fluid will result in a difference in kinetic energy and pressure between those two locations that is described by conservation laws.
• Bernoulli’s equation describes the conservation of mechanical energy in fluid flow. Relevant equation:
• Torricelli’s theorem relates the speed of a fluid exiting an opening to the difference in height between the opening and the top surface of the fluid and can be derived from conservation of energy principles. Derived equation: BOUNDARY STATEMENT All fluids will be assumed to be ideal, and all pipes are assumed to be completely filled by the fluid, unless otherwise stated. AP Physics 1: Algebra-Based Course and Exam Description Laboratory Investigations AP PHYSICS 1