BMEN90036 Biofluid Mechanics Assignment 1
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
BMEN90036 Biofluid Mechanics
Assignment 1
Dialysis
There is a total of 40 marks obtainable for this assignment. This assignment will contribute 10% to your final grade at the end of this semester. Please submit via the LMS a zipped folder containing your solu- tions to problems (scanned written solutions in .pdf/.docx formats are accepted) and any accompanying MATLAB scripts (.m files).
Figure 1: Patient connected to dialysis machine.
Kidneys are the body’s natural filter to remove waste and balance important minerals in the blood. When kidney functionality is reduced or compromised, one solution is a process called dialysis (Figure 1). In this process, blood is removed from the body, filtered through a dialyser (commonly called an “artificial kidney”), and then returned to the body.
In this assignment, we shall analyse a dialysis piping diagram (Figure 2). Blood is first extracted from the vein, then mixed with a stream of blood thinner diluted in a saline solution. A pump is used to drive the blood through the filter (dialyser) and then back into the patient’s bloodstream. For this analysis, we will only focus on the following three flow rates:
● The flow rate of the blood extracted from the vein, QV
● The flow rate of the blood thinner & saline solution, QS
● The flow rate of these two combined streams into the filter (dialyser), QF
Specifications:
Assume that the density of all fluids in this analysis is 1060 kg/m3 . The viscosity of blood before the addition of blood thinner is 5 cP. With the blood thinner applied, its viscosity reduces to 1 cP. The viscosity of the blood thinner itself can also be assumed to be 1 cP. The flow rate of blood extracted from the vein for a typical dialysis setup is 350 mL/min. The diameter of all tubing in the system is 3 mm, and for smooth plastic tubing, the roughness e is 0.0015 mm. The gate valves when fully open are characterised by K = 0.15, while the elbows in the system are characterised by 
= 40.
|
Pressure Tubing length Elevation from floor Flow rate [mL/min] |
PV = 10 kPa LV = 0.5 m zV = 1 m QV = 350 mL/min |
PS = 24 kPa LS = 2 m zS = 2.5 m QS =? |
PF = 1 kPa LF = 3 m zF = 3 m QF =? |
The tubing lengths are denoted V , S, or F , indicating the line from the vein to Point J, the line from the blood thinner & saline solution to Point J, and the line from Point J to the filter (dialyser), respectively.
Figure 2: Piping diagram for dialysis (not to scale).
Question 1 [18 marks]
Using the information provided, determine the unknown volumetric flow rates QS and QF [mL/min], the required pump head hP [m], and the power [W] required to drive the pump motor assuming a mechanical efficiency of 58%. Follow the instructions below:
● Write MEB equations for the pipelines and apply the continuity equation at Point J.
● Demonstrate an iterative method to solve these (if required) - this should be done via MATLAB code. For all turbulent friction factors (Re > 3000) required in the solution process, use the Colebrook-White equation reported below (note that fD is the Darcy-Weisbach friction factor; all other symbols have their usual meaning):
= 一2 log10 ╱ 
+ 
、
● Consider the major and minor frictional losses associated with the pipe, elbows, and valves as shown in the schematic diagram.
● State all assumptions made in the solution process.
Question 2 [12 marks]
(a) Using the information previously provided, write MATLAB code to generate the system characteristic
curve (system head vs. flow rate, Q) over a range of flow rates from 0 to 1200 mL/min. The system head is the head required for pumping. To simplify the solution process, assume that the pressure at Point J calculated in Question 1 remains constant.
(b) Using the theoretical pump head hP calculated in Question 1, determine the actual pump head
assuming a hydraulic efficiency of 95%.
2022-09-09