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# ecm 7 soln - ρ is the density of the suspending fluid and...

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ECM 5 Winter, 2009 Problem Set 7 Due 2/2/09 This problem set asks students to continue thinking about dimensions and units. . 1. Emulsions consist of small droplets of one liquid suspended in a second liquid. There are many examples of emulsions in our everyday life, e.g., milk and shampoo. Droplets of one liquid in another move under the force of gravity according to: V = 2 3 " + 1 3 " + 2 # \$ % ( a 2 g( ) drop * ) ) μ Here, V is the velocity of the drop, λ is the ratio of the viscosity of the liquid in the drop to that in the liquid in the suspending (outside the drop) fluid, a is the radius of the drop, g is gravity, ρ drop is the density of the drop,
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Unformatted text preview: ρ is the density of the suspending fluid and µ is the fluid viscosity. a. Show that this equation is dimensionally homogeneous b. In the limit of a very viscous liquid drop (drop viscosity goes to infinity), show that this equation reduces to the equation in Problem set 6 for a solid sphere c. Consider a 5 µ m diameter drop of olive oil in water. What is its velocity? What is its Reynolds number? 2. Consider the following equations: a. Work = Force times Distance b. Kinetic Energy = (mass x velocity squared)/2 c. Potential Energy = mass x gravity x height Show that all of these have the same dimensions...
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