Problem 4. A major transmission pathway of the novel coronavirus disease 2019 (COVID- 19) is through droplets and aerosols produced by violent respiratory events such as sneezes and coughs (Fig. 1). For the purpose of providing public health guidelines, we would like to estimate the amount of time it takes for these droplets to settle from air to the ground. The relevant parameters are the settling time (ts), the initial height of the droplets (H), gravitational acceleration (g), density of the droplets (pa), radius of the droplets (R), as well as dynamic viscosity of the ambient air (Pair). Use dimensional analysis and the Buckingham theorem to answer the following questions: 1. Find the independent dimensionless parameters using the table method. Then, express the settling time as a function of the other relevant parameters. Your solution should match the physical intuition that the settling time scales linearly with the initial height. 2. How would the settling change if the diameter of the droplet is doubled? 3. Given the constant that emerges in the dimensional analysis to be equal to 4.5, find the settling time of an 1 μm droplet created by an adult who is 1.7 m tall. The density of the droplets are p = 1.5 g/mL, and the dynamic viscosity of air is pair 1.81 x 10-5 Pa-s. t=0.11 s 5 cm Figure 1: High-speed imaging of droplets produced by a sneeze.
Problem 4. A major transmission pathway of the novel coronavirus disease 2019 (COVID- 19) is through droplets and aerosols produced by violent respiratory events such as sneezes and coughs (Fig. 1). For the purpose of providing public health guidelines, we would like to estimate the amount of time it takes for these droplets to settle from air to the ground. The relevant parameters are the settling time (ts), the initial height of the droplets (H), gravitational acceleration (g), density of the droplets (pa), radius of the droplets (R), as well as dynamic viscosity of the ambient air (Pair). Use dimensional analysis and the Buckingham theorem to answer the following questions: 1. Find the independent dimensionless parameters using the table method. Then, express the settling time as a function of the other relevant parameters. Your solution should match the physical intuition that the settling time scales linearly with the initial height. 2. How would the settling change if the diameter of the droplet is doubled? 3. Given the constant that emerges in the dimensional analysis to be equal to 4.5, find the settling time of an 1 μm droplet created by an adult who is 1.7 m tall. The density of the droplets are p = 1.5 g/mL, and the dynamic viscosity of air is pair 1.81 x 10-5 Pa-s. t=0.11 s 5 cm Figure 1: High-speed imaging of droplets produced by a sneeze.
Solid Waste Engineering
3rd Edition
ISBN:9781305635203
Author:Worrell, William A.
Publisher:Worrell, William A.
Chapter8: Landfills
Section: Chapter Questions
Problem 8.13P
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Transcribed Image Text:Problem 4. A major transmission pathway of the novel coronavirus disease 2019 (COVID-
19) is through droplets and aerosols produced by violent respiratory events such as sneezes
and coughs (Fig. 1). For the purpose of providing public health guidelines, we would like
to estimate the amount of time it takes for these droplets to settle from air to the ground.
The relevant parameters are the settling time (ts), the initial height of the droplets (H),
gravitational acceleration (g), density of the droplets (pa), radius of the droplets (R), as well
as dynamic viscosity of the ambient air (Pair). Use dimensional analysis and the Buckingham
theorem to answer the following questions:
1. Find the independent dimensionless parameters using the table method. Then, express
the settling time as a function of the other relevant parameters. Your solution should
match the physical intuition that the settling time scales linearly with the initial height.
2. How would the settling change if the diameter of the droplet is doubled?
3. Given the constant that emerges in the dimensional analysis to be equal to 4.5, find the
settling time of an 1 μm droplet created by an adult who is 1.7 m tall. The density of the
droplets are p = 1.5 g/mL, and the dynamic viscosity of air is pair
1.81 x 10-5 Pa-s.
t=0.11 s
5 cm
Figure 1: High-speed imaging of droplets produced by a sneeze.
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