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BME 2000 Introduction to Biomedical Engineering – Conservation of Mass
Homework #2 (20 points)
Be sure to include all work and use appropriate units. You should report quantitative answers in appropriate significant figures and box your final answer. Please use the problem solving framework for all problems in this set.
1.
(
5 points
) Use the Problem-Solving Template
for this question for full credit:
The blood bank currently has a critical shortage of blood, so you make an appointment to donate
(thank you!) While donating, they learn that you know how to do mass calculations and offer you a position to help prepare the blood for transfusions. For the first transfusion, you have the following three processed blood packs available:
Pack A
: Enriched in red blood cells (RBCs)
4.5 wt% white blood cells (WBCs); 50.0 wt% isotonic fluid; the rest is RBCs.
Pack B
: Enriched in serum proteins 50.0 wt% serum proteins; 3.0 wt% WBCs; 15.0 wt% isotonic fluid; the rest RBCs.
Pack C
: 100.0 wt% isotonic fluid
All three packs must be mixed in the correct proportions to generate blood for a transfusion pack. The transfusion pack needs to have the following composition: 3.0 wt% WBCs and 14.0 wt% serum proteins. Use the Assemble, Analyze, Calculate, Finalize framework
to organize and show your work. Answer the following:
a.
What is the basis in your solution to this problem?
b.
Write out mass accounting equations for RBCs, WBCs, isotonic fluid, serum proteins, and
total mass.
c.
Calculate the weight percents (wt%) of RBCs and isotonic fluid in the transfusion pack.
d.
What is the ratio of the mass of pure isotonic fluid (Pack C) to the mass of Pack A? What
is the ratio of the mass of Pack B to the mass of Pack A? 1/3
2.
(
6 points
) Use the Problem-Solving Template
for this question for full credit:
Arterioles bifurcate, or split, into capillaries within the circulatory system (
see Fig 1
). Using ultrasound, a technician notes that blood is flowing at a velocity of 30.0 cm/s through a particular arteriole with a diameter of 0.20 cm. This vessel bifurcates into two vessels: one with a diameter of 0.16 cm and a blood flow velocity of 25.0 cm/sec, and one with a diameter of 0.14 cm. Each of these two vessels split again. The 0.16cm diameter vessel splits into two vessels, each with a diameter of 0.12 cm. The 0.14cm diameter vessel splits into two vessels, each with a diameter of 0.11cm. Follow the diagram and labels shown in Figure 2
.
Determine the mass flow rate and velocity of blood in each of the four vessels at the end of the arteriole bifurcations
. Use the Assemble, Analyze, Calculate, Finalize
framework to organize and show your work. Be sure to state your basis
. Note: you may need to set up several systems, each with a different system boundary, in order to solve this problem. Figure 1
: Bifurcation of blood vessels throughout the body. Figure 2: Diagram of arterioles being observed in this problem. 2/3
3.
(
9 points
) Use the Problem-Solving Template
for this question for full credit:
After graduating with your bachelor’s degree in Biomedical Engineering, you go on to complete four years of medical school, followed by four more years of residency in anesthesiology. Today’s your first day as an attending anesthesiologist– CONGRATS!! You are responsible for preparing IV solutions containing various concentrations of drugs, and it is a good thing you remember mass conservation from BME 2000. There are three continuous streams available in the operating room, listed below, with their known mass fractions (for example: w
i,x
is the mass fraction of compound x in stream i).
Stream 1: water, salt (w
1,s = 0.050)
Stream 2: water, salt (w
2,s
= 0.040), Drug A (w
2,A
= 0.20)
Stream 3: water, salt (w
3,s = 0.030), Drug A (w
3,A
= 0.060), Drug B (w
3,B
= 0.090)
Your goal is to mix the above streams to produce an IV stream (Stream 4) under continuous operation that contains water, salt, Drug A, and Drug B with the following characteristics:
Drug A has a mass fraction of 0.030 (w
4,A
= 0.030)
The ratio of the mass fraction of Drug A to the mass fraction of Drug B is 3.0
Use the Assemble, Analyze, Calculate, Finalize
framework to organize and show your work. Answer the following
:
a.
What is the basis in your solution to this problem?
b.
Write a species mass conservation equation for each of the four constituents (water, salt, drug A, and drug B). Each term in the conservation equations should be written as a
constituent mass flow rate (e.g., •m
2,s
or w
2,s
•m
2
where 2 represents stream 2 and s represents salt – note the dot should be above the m’s to indicate flow rates). c.
What are the mass flow rates of each of the four streams? d.
Determine the mass fraction of each of the constituents (water, salt, drug A, and drug B)
in the prepared IV stream (stream 4) leaving the mixer. e.
Are your results reasonable? Justify.
3/3
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