WorksheetsProva di esame ATP 23 Dicembre 2020
Total questions: 10
Worksheet time: 36mins
(2 min) The stress tensor T in a Newtonian fluid of viscosity eta, contained between two horizontal parallel plates separated by a distance H, and moving in opposite directions with velocities U e -U is given by:
(3 min) A horizontal cylinder filled with water is rotated around its axis with angular velocity omega. Using cylindrical coordinates, the velocity vector and the stress tensor are given by:
(3 min) We want to prove that the cross-section area, Sjet, of the free jet of a Newtonian fluid is smaller than the cross section of the pipe, Sp, where the jet exits from (see figure). If vp,avg is the average velocity inside the pipe (where a parabolic, laminar flow profile develops) and vjet is the uniform velocity of the jet (where a flat velocity porofile is present), which set of equations is valid and can be used the prove the above statement?
(5 min) A Newtonian fluid is placed between two parallel disks of radius R (see figure). The bottom disk is rotated, whereas the upper disk is held fixed. Assuming steady-state creeping flow, the torque necessary to move the bottom plate when the disk radius is one half of the original value is given by
16 times smaller
8 times smaller
4 times smaller
2 times smaller
(5 min) When coating a solid film through a converging die we consider a rectangular cross section die of length L, heigth H(x) changing along the flow direction x, and width W). If y is the coordinate along the H direction perpendicular to x, with origin on the surface of the film, the force necessary to pull the film is given by:
(3 min) A Newtonian fluid of viscosity mi and density rho is mixed in a tank of diameter D by a rotor that rotates at an angular velocity omega. Which dimensionless group can be formed by using the above parameters?
(5 min) If A and B are two tensors, their scalar product does not enjoy the commutative property. Which of the following expressions is correct?
(5 min) It is well known that the flow of a fluid around a sphere generates a friction force on the sphere. Let us assume that the Navier-Stokes equations for the problem have been solved. Therefore, the velocity and the pressure fields are known everywhere. Starting from the above point, describe the steps that must be taken to calculate the friction force acting on the sphere. Try to be as descriptive as possible. It is not necessary to write equations, but to explain concepts.
(3 min) A liquid and a gas flow under the action of gravity through an inclined channel of rectangular cross section. The liquid occupies the bottom part of the pipe. What is a realistic, qualitative velocity profile across the channel?
(2 min) A fluid flows through a vertical pipe characterized by a sequence of a sudden contraction and a sudden expansion (see figure). The pipe diameters D in the upstream and downstream sections are equal. H is the difference in altitude between the inlet and outlet sections. Assuming negligible viscous losses, if v1, p1 and v2, p2 are the velocity and the pressure at the inlet and outlet sections, which of the following statements is true under steady-state conditions?
v1= v2 and p1< p2
v1= v2 and p1> p2
v1= v2 and p1= p2
v1> v2 and p1< p2
