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#### The hovering squid

A laboratory model of squid locomotion, shown in the figure, uses an internal propeller to inhale water from the side of the model and inject it from the outlet, having a diameter D = 15 mm. The model weighs 2.5 N and has an average specific gravity of 2.5. When the model is submerged, 20% of its entire volume is occupied by the solid walls, propeller etc., while the remaining 80% is filled with water.
a) Determine the mass flow rate through the model that will permit it to remain motionless in water while having its axis vertical and its outlet pointing downwards.
b) While maintaining the same mass flow rate as the one calculated in (a), the model is suddenly turned around such that its outlet faces upwards. Determine its initial acceleration.
c) Now consider that the model is oriented again as in part (a), but that the mass flow rate is increased to twice the value calculated above. Further consider that the drag force FD from the water can be calculated as:

FD = ½ ρ CD A V2

where ρ is the density of water, CD is a specified drag coefficient, A is the projected area of the model (also specified) and V is the velocity of the model. Write a differential equation for the velocity of the model. Do not attempt to solve it, but describe the steps that you would undertake to solve this equation. Would you expect the speed of the model to reach a constant value after some time? If so, explain why. Express any other thoughts that you have on this problem.

Contributed by Stavros Tavoularis, Department of Mechanical Engineering,
University of Ottawa, Ottawa, Canada.

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