Answer to Question #154483 in Physics for Himanshu Aggrawal

Question

1 Consider a vessel with a diameter of T=0.9 m, and a ratio of the propeller diameter to vessel diameter equal to 0.37. Consider the height of the vessel H-T. The working fluid has a density of 1100 kg/m and dynamic viscosity 0.022 Pas. Determine:

(a) The rotation frequency N (in rpm) needed to reach a Reynolds number of 10

(b) The power in kW) corresponding to the frequency computed in point (a) and to a power number of 2.5

(c) The specific mean dissipation rate as well as the Kolmogorov length scale

3 marks

3 marks

3 marks

(d) By reference to figure I, at a Reynolds number of 10, which types of impeller should we 3 marks use for the power number to be in the range 2.5 - 3? Also, which impeller would you chose to maximise the power number at the same Reynolds number?

(c) If we are to further increase the power number beyond the maximum value observed in 2 marks figure 1 for the same type of impeller and diameter, which modification would you need to provide to the impeller?

(f) Assume we want now to scale up the vessel by a factor of 15. maintaining a similar 6 marks geometry, to match conditions in a plant. Determine the power requirement in the plant in order to have a similar mixing time with respect to the lab scale vessel, for which the power was computed in point (b), and assuming the same frequency N computed in point (a). Also, compute the Reynolds number corresponding to the plant vessel.

(g)

If we need to decrease the power with respect to the value computed in point (1) by 10%, 5 marks how much the frequency N will need to vary in order to have the same power number?

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Figure Q1

Answer 1

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