In an experimental study designed to simulate the manner in which a cat drinks,

Question

In an experimental study designed to simulate the manner in which a cat drinks, a glass plunger simulating a cat's tongue just makes contact with the free surface in a pan of water. The plunger then oscillates vertically, causing a column of water to rise and eventually be pulled back down by gravity. The oscillation frequency, w(omega), depends upon surface area of the plunger, A, plunger velocity, U, acceleration of gravity, g, water density, p(roh), and surface-tension coefficient (sigma). How many dimensionless grouping are there? What are the dimensionless groupings?

Explanation / Answer

WE KNOW: In a dimensionless group is any combination of dimensional or dimensionless quantities possessing zero overall dimensions. Dimensionless groups are frequently encountered in engineering studies of complicated processes or as similarity criteria in model studies. A typical dimensionless group is the Reynolds number (a dynamic similarity criterion), NRe = VD?/µ. Since the dimensions of the quantities involved are velocity V: [L/T]; characteristic dimension D: [L]; density ?: [M/L3]; and viscosity µ: [M/LT] (with M, L, and T as the fundamental units of mass, length, and time), the Reynolds number reduces to a dimensionless group and can be represented by a pure number in any coherent system of units. See Dynamic similarity Many important problems in applied science and engineering are too complicated to permit completely theoretical solutions to be found. However, the number of interrelated variables involved can be reduced by carrying out a dimensional analysis to group the variables as dimensionless groups.

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