Question

Thankfully, you were able to reconnect your air tube before you lost consciousness. After such a stressful situation, you decided to take a vacation. On your vacation, you are sitting on a beach on Earth drinking a cocktail (a non-alcoholic one, of course). It's one of those fancy drinks with a straw, as shown below on the left. As an engineer who is fascinated by fluid flow, you start wondering about the velocity profiles within the fluid that you create by moving the straw. To simplify your analysis, you assume that the glass and the straw can be modelled as two infinitely long concentric cylinders, as shown in the middle picture of the schematic. The inner cylinder has a radius of R, and the outer cylinder has a radius of R2. The space between the inner and outer cylinder contains only a Newtonian fluid (no ice). Additionally, assume that the cylinders are vertical so that gravity is acting only in the axial direction. Now imagine that the outer cylinder is stationary and the inner cylinder is moving upwards in the positive z-direction with a velocity of V, as shown in the image on the right. Straw V R2 R1 Fancy drink View from the top Side view A. Sketch the steady state velocity profile of the fluid. In which directions are the fluid flowing? In which directions are there gradients in the fluid velocity? (6 marks) Derive an expression that can be used to solve for the velocity profile within the fluid. Evaluate the expression at R, and R2 to illustrate that it fulfils the boundary conditions B. (30 marks) one sch if the fluid were sketch the a shear id, C ng (ii) a shear thickening fluid, and (iii) a Bingham plastic. Label each velocity profile. In one to two sentence each, explain how the flow of each of the fluids would differ from that of a Newtonian fluid. (6 marks)

Answer 1

A V - velacil apward direstnCraieadi in the Fids 211 3l Radal dipıckrmu Cove ow aptoimated ai a nvisous At T: o, u: V Seandary tditions ..

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