Chapter 2 - Foundations of
Conservation Principles
OVERVIEW
The fundamental framework for the conservation laws and system definitions are described in Chapter 2. Explicit discussion on isolating the system of interest and labeling the system boundary and surroundings is given. Algebraic, differential and integral forms of the accounting and conservation equations and the rationale for using each are presented. The generic form of the accounting equation is as follows:
Input - Output + Generation - Consumption = Accumulation
and the generic form of the conservation equation is as follows:
Input - Output = Accumulation
Since a conserved property can neither be created nor
destroyed, conservation equations can be written for total mass, elemental
mass, linear momentum, angular momentum, net charge, and total energy. Real-life examples such as balancing a
checkbook, population growth, and the drainage of water from a bathtub are
given. In addition, several biomedical
examples are given. The system
definitions of open, closed, isolated, reacting, non-reacting, steady-state and
dynamic are illustrated with examples.
EXAMPLE PROBLEMS
1. Do the following for each part (a.-c.):
i. Draw a picture of the system.
ii. Name a property that can be counted.
iii. Label the system, surrounding, and system boundary.
iv. State the time period of interest.
v. Identify the system as open, closed, or isolated and state why.
vi. Identify the system as steady-state or dynamic and state why.
vii. Identify the system as reacting or non-reacting and state why.
viii. Which of the following equations can be used to describe the system: algebraic, differential, integral. (More than one type of equation may be appropriate.)
ix. Is the selected property (part ii) conserved in this system? State why.
Explain your justification for each selection. (There can be more than one “right” answer; it depends on how you set up the system.)
a. Blood is flowing through the heart. Consider the inlets to the heart as the pulmonary vein and the vena cava and the outlets from the heart as the pulmonary artery and the aorta. Ignore the coronary artery and cardiac veins. You want to write a model of the blood flowing through the heart that considers changes that occur second by second (i.e. a model that looks at different points in the cardiac cycle).
b. A heart-lung by-pass machine is used to circulate blood through the body during open heart surgery when the heart is stopped. Flowing blood enters and leaves the by-pass machine. Special biocompatible material is used to line the walls of the machine so that no reactions in the blood occur. Energy in forms of heat and mechanical work enters the by-pass machine as well. During an operation, the by-pass machine is maintained at constant temperature and other operating conditions. You are interested in writing an accounting equation on the energy in the by-pass machine.
c. The effects of osmotic water shifts on red blood cells (RBC) can be observed easily experimentally by exposing red blood cells to hypertonic and hypotonic saline solutions. The inner fluid of red blood cells is isotonic with 0.15 M NaCl. When RBCs are placed in an hypertonic solution, water leaves the cells, causing them to shrink. When RBCs are placed in a hypertonic solution, water enters the cells, causes rapid swelling, which may result in the bursting of some cells. An aliquot of 105 red blood cells is added to 1 L of saline with a concentration of 0.05 M NaCl. Assume that no metabolic activity in occurring in the RBCs to generate water. You are interested in writing an accounting equation on the water in the RBC as a function of time. Will the size of this system change?
2. A patient in the hospital is being given a saline solution through an IV. Each day, the patient receives 1200 g of water through the IV. The patient receives water through no other means. A catheter collects all the urine leaving her bladder. It is determined that the daily water loss in the urine is 1600 g. Assume that water leaves her body through no other means. Metabolic activity is known to be normal.
While in the hospital for a week, the doctor notices that the patient loses no weight. (From this, assume that the mass of water in the body does not change with time.) Yet, a quick mass balance looking at only the inlet and outlet terms of the water doesn’t make sense. Help the doctor figure out what is going on by defining whether the system is open or closed, steady-state or dynamic, reacting or non-reacting. What is going on? Try to find some biological evidence to support your hypothesis. Finally, write the accounting equation with appropriate terms to describe the water balance in the patient.
Chapter 1 - Introduction to Engineering Calculations | Chapter 3 - Conservation of Mass