Chapter 7: Problem 6
Why, on a winter morning, do wood floors feel more comfortable than stone floors?
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These are the key concepts you need to understand to accurately answer the question.
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Chapter 7: Problem 6
Why, on a winter morning, do wood floors feel more comfortable than stone floors?
These are the key concepts you need to understand to accurately answer the question.
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Use dimensional analysis to estimate the diffusion time \(t\) based on \(L\) (the relevant characteristic of the room) and \(D\) (the characteristic of the random walk).
In most American states and many countries, newborn babies are tested for the metabolic defect phenylketonuria (PKU). The prior odds of having PKU are about 1 in 10000 . The test gives a false-positive result \(0.23\) percent of the time; it gives a false-negative result \(0.3\) percent of the time. What are Pr (PKU | positive test) and Pr (PKU | negative test)?
In this problem, you use momentum flux (Problem \(7.25\) ) to estimate the drag force on a sphere of radius \(r\) in a flow at low Reynolds number \((\operatorname{Re} \ll 1)\). If \(\operatorname{Re} \ll 1\), the boundary layer (Section \(7.3 .4)\) - the region over which the fluid velocity changes from zero to the free-stream velocity \(v\) -is comparable in thickness to \(r\). Using that information, estimate the viscous drag force on the sphere.
Estimate the diffusion constant for air molecules diffusing in air by using $$ D \sim \frac{1}{3} \times \text { mean free path } \times \text { travel speed } $$ and the mean free path of air molecules (Section 6.4.5). This value is also its thermal diffusivity \(\kappa_{a i r}\) and its kinematic viscosity \(v_{a i r} !\)
If a quantity a has the plausible range \(1 \ldots 4\), and the quantity \(b\) has the plausible range \(10 \ldots 40\), what are the plausible ranges for \(a b\) and for \(a / b\) ?
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