# Murray’s Principle of Minimum Work

by | Aug 25, 2022 | Physics, Experiments

Contents

## Introduction

The Murray’s principle of minimum work can only be applied to a circular cross-section vessel. Therefore, in this experiment, we will be replacing the circular cross-section with a rectangular cross-section to obtain a better result. This will also distinguish the naturally occurring vessel (circular cross-section) from the artificially constructed vessel.

## Aim

To determine the factors that can maximise the conductance of a microfluidic network of a given volume.

## Theory

1. Organ transplantation is a very useful modern-day technique to transplant the organ of someone infected with lungs and other organs-related issues.

2. Under this comes to tissue engineering that creates artificial organs because of the unavailability and irregularity of organ donors.

3. But this engineering faces a big issue with designing organs that can perform all the normal organ activities.

4. These artificial organs consist of a large number of branching networks of microfluidic channels.

5. Scientists proposed Murray’s Law because of the resemblance between the branching structure of blood vessels in mammals and the artificial construction of organs.

6. This governs the application of the geometrical shape of mammal organs to the artificial organ design.

7. According to Murray’s principle, the flow rate of a liquid or solid through a bifurcating organ is maximised by making the diameter of the daughter vessel tapper down by the cube root of two from the parent vessel. 1. A computer

2. Notebook

3. Pen or pencil

## Procedure

Step 1: Use Ohm’s law for current flow.

Step 2: Use Hagen-Poiseuille for fluid flow.

Step 3: Use the above formulas to derive the overall conductivity of branching fluid networks.

Step 4: Next, write down a small program to sweep the geometrical factors to a longer range.

Step 5: Using this program, look for the peak.

Step 6: Record your observations.

## Observation

1. We observed three important things those are.

2. The tapering rules, when a rectangular channel was square, were the same as depicted in Murray’s law for circular channels.

3. Tapor factor was the function of the aspect ratio of the parent channel for maximising the bifurcation hydraulic conductance. This was for the more general rectangular networks.

4. The conductance of bifurcation was the peak function of the taper factor. This was for the higher-order network.

## Result

1. Murray’s principle applies only to bifurcating channels, a network of artificial rectangular channel networks to circular cross-sections.

2. The microfluidic conductance of a given volume can be maximised by selecting the proper geometrical scale factors.

## Precaution

1. Take help in creating the program.

2. Use all the formulas correctly.

## Conclusion

In this experiment, we showed that the microfluidic network conductance of a volume could be enhanced by selecting a proper geometrical shape.

## Viva Questions With Answers

Q.1 What was the aim of your experiment?

ANS. We aimed to show how the proper selection of geometrical factors can maximise a microfluidic network conductance volume.

Q.2 What is Murray’s principle?

ANS. Murray’s law state that the flow rate through a bifurcating organ maximises by making the diameter of the daughter vessel tapper down by the cube root of two from the parent vessel.

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