Evacuated Canister and Flow Rate

[Dylano]

Hello everyone, I am currently in a mechanical engineering program, and I am on my first co-op work term. I have been assigned to make modifications to a PVC collection device involving flow rates, but I have not yet taken any courses relative to flow. I was hoping I could get some help and some explanations of the theory involved.

So I have a PVC canister, with a volume of 1 litre. The canister is evacuated to -26 inches of mercury. The canister is then attached to a series two of plastic tubes to restrict the air flow. The first tube has a inner diameter of 1.58 mm and a length of 60 cm. The second tube has an inner diameter of 0.0635 mm and has a variable length. Then the system is open to normal atmospheric pressure.

The goal of this apparatus is to collect samples of air over a 24-36 hour time period. I am looking for some way to model this so that I can perform calculations with different volumes/diameters of tube/etc. I am really unsure how to do this as the pressure inside the canister is changing, which would also affect the flow rate (I am assuming).

Thanks!

 

[Valerie Park]

To model this system, you will need to utilize the principles of fluid mechanics. The most important equation to consider is the continuity equation. This equation states that mass flow rate through a pipe or tube is equal to the cross-sectional area of the pipe multiplied by the average velocity of the fluid. Since the pressure inside the canister is changing, you will have to consider Bernoulli's equation as well. This equation states that the sum of pressure, kinetic energy, and potential energy is constant throughout the system. This equation can be used to determine the pressure difference across the two tubes, which in turn can be used to calculate the flow rate. Finally, you will need to consider the effects of friction on the flow. As the fluid moves through the tubes, it experiences frictional forces, which cause the fluid to lose energy. The amount of energy lost due to friction depends on the type of fluid, the length of the tube, and the diameter of the tube, among other factors. To accurately calculate the flow rate, you will need to take these factors into account. I hope this helps!