• BME 200
  • Systems and Control Volumes

    Systems and control volumes

    If we wanted to create a mathematical model of blood flow in an artery, we would first need to define our system. A system is the matter or region in space that we wish to study. A system is separated from its surroundings by a boundary. The surroundings are the regions outside the system. The boundary is an imaginary line (or surface) that separates the system from its surroundings.

    Figure 1. A cross-section of an artery. The system we wish to study is the blood within the artery. The system boundaries are along the top and bottom arterial walls and the entrance and exit of the artery.

    Mass can cross the boundary of an open system. No mass can cross the boundary of a closed system. A normal, healthy artery is an example of an open system because blood enters at one end and exits at the other. An artery occluded at both ends is an example of a closed system.

    Figure 2. In an open system, mass can cross one or more boundaries of the system. In a closed system, no mass can cross the boundaries.

    An open system is also called a control volume (CV). A CV can move over time and change its shape. We might use a moving CV if we wanted to follow a particular region of blood as it flows through a vessel. Likewise, if we wanted to analyze the blood flow through an aneurysm, a CV that changes size over time would be appropriate.

    Figure 3. An aneurysm is a weak spot in the wall of an artery that grows in size over time. In this system, the CV grows larger with time.

    Last updated:
    August 23, 2018