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Two problems: Dimensional analysis and Flow of fluid in pipe

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1. The thickness h of a puddle of water on a waxy surface depends on the density ρ of the liquid, the surface tension γ (SI units: N/m) and another physically which is gravity, g. Use dimensional analysis to find a relationship between the thickness and the other 3 variables. (I.e make a proportionality relationship that make sense dimensionally) e.g,
h ∝ [a combination of the physically relevant parameters that has dimensions of length]

2. The Canadian Norman Wells Oil Pipeline extends from Norman Wells, Northwest Territories, to Zama, Alberta. The 8.68 x 10^5 m-long pipeline has an inside diameter of 12 in, and can be supplied with 35 L/s.
(a) What is the volume of oil in the pipeline if it is full at some instant in time?

(b) How long would it take to fill the pipeline with oil if it is initially empty?

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The formula for the thickness of water puddle is derived using dimensional analysis is determined. The rate of volume flow through a pipeline is calculated.

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