In the rain with and without an umbrella? The Reynolds transport theorem to the rescue

Abstract

The age-old question of whether to run or walk in the rain still raises interest because of its practical relevance. A number of published studies have been carried out to address this question. These studies showed that there is no trivial answer and that different factors, including the rain conditions (rate and angle), the walking/running speeds and even the geometry used for analysis and the shape of the person matter. In the present paper, we present an analysis of the rate and amount of rain accumulation on a person walking/running through the rain using the Reynolds transport theorem (RTT) and its implementation for mass conservation. A new twist to earlier analyses is added, which involves the usage of a simplified model for an umbrella. The present work illustrates the use of RTT to establish the observations made using different analyses as well as demonstrates the RTT problem with this new twist.