Calculate the normalized distribution (µm-1 cm-3) and plot it as a function of t

Question

Calculate the normalized distribution (µm-1 cm-3) and plot it as a function of the diameter (µm) and the logarithm of the diameter. Which plot is better? Why? Calculate the cumulative distribution and plot it in the same way as in the previous case. The first two values are provided. What does the last value of the cumulative distribution indicate?

Find the diameters first and then use the logarithm to easily plot it.

1. Aerosol size information: Size Range, m Concentration, cm3 Cumulative, cm3 100 200 30 20 40 60 200 180 60 20 100 300 0.001- 0.01 0.01-0.02 0.02 0.03 0.03- 0.04 0.04 0.08 0.08-0.16 0.16-0.32 0.32 - 0.64 0.64 1.25 1.25 - 2..5 2.5- 5.0 5.0-10.0O Calculate the normalized distribution (um1 cm3) and plot it as a function of the diameter (um) and the logarithm of the diameter. Which plot is better? Why? Calculate the cumulative distribution and plot it in the same way as in the previous case. The first two values are provided. What does the last value of the cumulative distribution indicate?

Explanation / Answer

A) Ans : because It will depend on the elastic properties of the tube, as well as on the inertia of the fluid. the tube’s elastic properties by its distensibility where A is the tube cross-sectional area, D is the tube diameter, p is the transmural pressure, and we have assumed that the tube cross-section remains circular and is proportional to the fractional change in tube diameter induced by a unit change in transmural pressure.the pulse wave speed c depends on artery distensibility and fluid density.

B)Ans: Reflection coefficients at the bifurcation.

Every time a pressure wave encounters a change in mechanical or geometrical properties of the vessel, a part of the forward pressure wave is reflected and backward propagating waves are generated. Although diffused reflections arise everywhere, bifurcations are the main source of reflections. In this regard, the bifurcation reflection coefficient can be assessed as :           

                            

where is the bifurcation-specific reflection coefficient and subscripts in and out refer to bifurcation inlet and the outlet sections.A positive (negative) reflection coefficient means that part of the forward pressure wave is reflected as a compression (expansion) wave, so that the backward pressure wave adds (subtracts) to the incident wave.

The characteristic impedance of the daughter arteries will in general be different from that of the parent artery, since c and A will differ from daughter to parent. This means that the ratio of the pressure pulse amplitude to the flow pulse amplitude must change as the pulse wave passes through the junction.the arteries and junction are treated as a one dimensional system in which pressure is uniform across the artery at each axial station, while pressure and flow rate vary axially.

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