Biofluid Mechanics (BMEN90036) Assignment 1

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Assignment 1

Biofluid Mechanics (BMEN90036)

The University of Melbourne

Instructions: Answer each of the following questions in a single document, containing any relevant workings. Please include appropriate figure axes labels in any plots. Equations may be handwritten. Attach (copy-paste) any code in an appendix in the same document.

Question 1 [30 marks]

To this point we have assumed that the height in tanks remains constant, which is appropriate for the case when we want to know the instantaneous flow rate for fluid moving between tanks. This is more complicated for analysing systems over longer timescales, however, when we want to know how the overall system evolves when the level in tanks change.

We want to fill a 0.5m diameter tank of a bioprocessing slurry (ρ = 1020 kg/m3 , µ = 0.0015 kg/ms) initially with a height of 2m to 6m using a pump operating with 82% mechanical efficiency and a brake power of 1500W if it is moving fluid from an immediately adjoining 1.5m diameter tank, initially filled to 2m. The pump and any entrance/exits to the tanks are located on the floor between the two tanks (at a height of 0m). The pump curve for this pump can be approximated by the equation hp = 20.2 – 0.02Q2 , where Q is the flow rate in m3 /h and hp has units of meters. Both tanks are vented to atmosphere. Because these tanks are so close together, you can ignore minor losses and friction effects from pipe tubing.

(Hint: you may not require all the values provided in the problem statement to calculate the answers to each of the following)

A. Potentially using a MATLAB script, calculate the amount of time to fill Tank 2 to the desired height. [20 marks]
B. What is the maximum (absolute) height to which the fluid could be pumped in Tank 2 (provided Tank 2 were sufficiently tall)?[5 marks]

C. Following on from your answer to part (A), take the case where there is now a pipe (5 cm diameter, surface roughness of 0.03 mm) connecting Tank 1 to the pump, which we can assume has an NPSHR of 2.8m. The fluid has a vapour pressure of 4.2kPa. Ignore minor losses associated with entry and exit of pipes. Find the longest this pipe can be beforecavitation occurs at any point in the pumping process for the situation described, where the height in Tank 2 is to be raised to 6m high.

For simplicity, you can assume the pump head from the pump curve for the tank height at which cavitation is most likely to occur, though you should state whether this assumption will yield an overestimate or underestimate of the actual pipe length.[5 marks]

Question 2 [30 marks]

To date we have explored iterative solutions in class to calculate flow rates and pressures for complex systems. However, this process can be tedious to do by hand, especially for systems of increasing complexity, where a computational solution can help to arrive at the correct solution much faster. For the case of a pipe network shown below containing water (density = 1000 kg/m3 , viscosity = 0.001 kg/m3 ),

A. State the direction of the flow between each of the Tanks (1,2,3) and the junction – is the flow moving into or out of each of the tanks, and why? Draw a diagram showing the direction of flow. (Hint: you should be able to determine this without any iterative solution using the information provided). [5 marks]

B. Using whatever approach is appropriate, including a MATLAB script, find the absolute value of the flow rate between each of the tanks and the junction. [25 marks]
You are given the following information:
the diameter of all pipes is 5 cm
the surface roughness of all pipes is 0.05 mm
the pressure in Tank 1 is 300kPa
the pressure in Tank 2 is 500kPa
the pressure in Tank 3 is 450 kPa
the length of the pipe from Tank 1 to the junction is 100 m
the length of the pipe from Tank 2 to the junction is 75 m
the length of the pipe from the junction to Tank 3 is 100 m
the height of the free surface in Tank 1 is 100 m
the height of the free surface in Tank 2 is 75 m

the height of the free surface in Tank 3 is 25 m

Question 3 [15 marks]

Carbon dioxide is often used in biomedical engineering labs for many applications, one of which is cell culturing. UltraSuperCell Services®is a large commercial laboratory, and requires large amounts of carbon dioxide. They have determined that it is much more efficient to pump this carbon dioxide from a neighbouring facility located 1000 m away via a long pipe with an internal diameter of 12 cm and a fanning friction factor of 0.005. The flow is isothermal at 25°C and carbon dioxide has the chemical formula CO2, where carbon has a molecular weight of 12g/mol and oxygen has a molecular weight of 16 g/mol. The neighbouring facility stores the carbon dioxide at a pressure 521 kPa and the lab requires the pressure to be 200 kPa.

A. What is the mass flow rate of the carbon dioxide? Show all working. [10 marks]

B. What is the maximum initial pressure that you would recommend in order to maximize the flow rate of carbon dioxide? Show all working. [5 marks]

Question 4 [25 marks]

Capillary microfluidics can deliver liquids in a pre-programmed way without the use of pumps, by exploiting surface tension effects encoded by the micro-channel. Inlet ports to capillary-based microfluidic chips are usually wide shallow structures that are open to atmosphere. If the channel material is hydrophilic, namely one with a contact angle (θc) less than 90°, fluid (with ρ = 1000 kg/m3 , µ = 0.001 kg/ms) will be drawn inside the channel. A diagram showing the initial and final states in the device cross-section are shown below. You can assume that the materials in contact with water outside the channel are hydrophobic (water-repelling) such that the fluid outside the channel remains spherical, that the exit of the channel is open to the air, and that θ

2023-10-05