1. For a soap bubble, the inside pressure must be greater than that outside, and the surface tension acts like a skin to support this pressure difference Ap. The pressure difference is then a function of surface tension σ and bubble radius R, i.e., Ap = f(o, R). Using Buckingham Pi theorem, find the II group(s) associated with this problem and express them in the form II₁ = (II2, ..., II-r). (Ans: ApR = constant) σ
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- The Ekman number, Ek, arises in geophysical fluiddynamics. It is a dimensionless parameter combining seawaterdensity ρ , a characteristic length L , seawaterviscosity μ , and the Coriolis frequency Ω sin φ , where Ωis the rotation rate of the earth and φ is the latitude angle.Determine the correct form of Ek if the viscosity is in thenumerator.In the following section, at least 2 to up to 5 answers may be correct. 1) For a fluid, the assumption (simplifying notion) of incompressibility has important consequences: Pascal’s principle: a change of pressure in an enclosed fluid at rest is transmitted undiminished to all points in the fluid. pressure changes are transmitted immediately from one place to another. the speed of sound then is infinite (just within this approximation). pressure becomes unpredictable. none of the above. 2) Archimedes’ principle can be summarized as: an immersed object is buoyed up by a force equal to the weight of the fluid it displaces. a bathtub is fun, and may lead to important physical discoveries regarding the volume of an object and how much water it displaces, and the weight of that amount of water. boats swim because of the work done by sailors. submarines are always doomed. fish swim because they are less heavy than water 3) A…For most gases at standard or near standard conditions, the relationshipamong pressure, density, and temperature is given by the perfect gasequation of state: p = ρRT, where R is the specific gas constant. For airat near standard conditions, R = 287 J/(kg · K) in the International System of Units and R = 1716 ft · lb/(slug · ◦R) in the English Engineering System of Units. Using the above information, consider the following two cases: a. At a given point on the wing of a Boeing 727, the pressure andtemperature of the air are 1.9 × 104 N/m2 and 203 K, respectively.Calculate the density at this point.b. At a point in the test section of a supersonic wind tunnel, the pressureand density of the air are 1058 lb/ft2 and 1.23 × 10−3 slug/ft3,respectively. Calculate the temperature at this point.
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