Question

4. When small aerosol particles or microorganism move through air or water, the Reynolds number is very small (Re << 1). Such flows are called creeping flows. The aerodynamic drag force, FD, on an object in creeping flow is a function only of its speed V, some characteristic length scale L of the object, and fluid viscosity u (see Fig. 4). Use the method of repeating variables to generate a relationship for Fp as a function of the independent variables. Draw a sketch to illustrate the problem solution and show all details of your work. (6 points) ३ V FO -L- - Figure 4
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Answer 1

Solution. In this problem we have following Four variables (n) = 4 Dimensional unit Dependent laziable). Doage force (F) ♡ M'i't-2 other variables. L' length (e) LITY Speed (V) viscosity (4) T T Milyt Sketch'a 4. leh So Number of fundamental quantities m= 3

Total Non-dimensional Numbers- m-na 4-3= Non-dimensional Number: IT,= fo[ (6) " (ujo pas] -0 MOLOTO AL'T? I (L')" (L' + tgb (M'Ent] Comparing powers on both sides M's power;- = t's power :--) -2-bocão = b = -1 L's 1 + a +b -C20 as-1 power in using a, b, c in ego This folleji (v) (45] TT, - FO Relationship for F in terms of other variables u ve