Prova di esame ATP 13 Gennaio 2021

(2 min) If α is a scalar field and T a tensor field, one has:

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(2 min) A liquid is flowing out of a open tank from a hole in the bottom. h is the height of liquid in the tank (constant with time) and g is the acceleration of gravity. The velocity of the fluid exiting the hole and the one that would results from neglecting all viscous losses respect the condition:

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(2 min) If A is an anti-symmetric tensor, its general form is:

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(3 min) We want to transport water at a flow rate of 10 L/s from one position to another position at an elevation 10 m higher than the first one. Neglecting the viscous losses we need a punmp with a power of:

• 1 kW

• 100 W

• 100 kW

• 10 kW

(3 min) Under steady-state conditions, the torque necessary to rotate the external cylinder of a coaxial cylinder viscometer (Couette) depends upon the radius R of the external cylinder raised to a power of:

• 2

• 1

• 0

• 3

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(5 min) A Newtonian incompressible fluid of viscosity eta flows radially between two discs. Neglecting boundary effects and assuming creeping flow conditions, the only non-zero velocity component is the radial one, namely v_r(r,z). The total fricion force F that the fluid exerts on both discs is:

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