Question

The range of aerosol size released during different expiration events are 0.5 to 256 pm. The different sizes of aerosol you could consider for the analysis are 0.5-1-2-4-8-16 – 32 - 64 - 128 - 256 pm. The speed of breathing is about 1.5 m/s, coughing ranges from 1.5 to 30 m/s, and sneezing 20 to 50 m/s [2]. Assume that the aerosols do not go through evaporation, and maintain a constant size. Also, assume the aerosols/droplets produced during the expiration events are made of water, thus have a density of 1000 kgm-3. • Assume the values of rest of the parameters like viscosity and density of air, acceleration due to gravity, etc., according to your judgment. Please state the values you end up using. Estimate the Reynolds number of jet coming out during breathing, coughing and sneezing. Which of these flows are laminar and which of them are turbulent ? For the given aerosol sizes, what is the maximum velocity of release that allows the aerosols to be moving as creeping (Stokes) flow? Assume the aerosols to be spherical. What is the distance traveled by aerosols of different sizes before hitting the floor, when they are released during different expiratory events from a height of an average human being (you can use your own height for the calculations) ? Can you also estimate the time that aerosols of different sizes takes to reach the floor ?

Answer 1

The Reynolds number can be calculated for breathing, coughing, and sneezing to determine if the flow is laminar or turbulent. The maximum velocity for creeping (Stokes) flow can be calculated for aerosols of different sizes. The distance traveled by aerosols before hitting the floor and the time taken can also be estimated.

Step-by-step explanation:

The Reynolds number is a dimensionless quantity that describes the flow of a fluid. It is calculated using the formula Re = (density × velocity × diameter) / viscosity. For the given values in the question, the Reynolds number for breathing, coughing, and sneezing can be calculated using the provided velocities and aerosol sizes.

The flow can be categorized as laminar or turbulent based on the Reynolds number. Generally, a Reynolds number below 2000 indicates laminar flow, while a Reynolds number above 4000 indicates turbulent flow. The values of the Reynolds number calculated for breathing, coughing, and sneezing can be used to determine the flow regime.

For aerosols to be moving as creeping (Stokes) flow, the maximum velocity must be such that the Reynolds number is below 1. This can be calculated using the provided aerosol sizes and the formula mentioned earlier.

The distance traveled by aerosols of different sizes before hitting the floor can be calculated using the equations of motion. The time taken for the aerosols to reach the floor can also be estimated using the calculated velocities and the known height.