Given laminar fully developed flow in an elliptical duct of semiaxes a and b. Show that, for a given pressure gradient, the flow rate per unit area is a maximum when a=b. 1. Answer the following questions:(a) What is the physical meaning of the following:D aDtwhere V is the velocity vector of the flow field.(b) Let the viscous stress tensor be denoted by 7. How is the surface (vector) force f, acting bythe fluid on a surface element ds (with unit normal în ) computed? Give your answer in vectornotation and also in index notation. What is the physical meaning of tyy ?(c) Write down the work done on a material volume of fluid by the viscous surface force invector notation and also in index notation.(d) Write down the amount of conduction heat flux 'q' (a scalar) on a surface element ds (withunit normal în ) in vector notation and also in index notation.2. Two plates and a fixed surface sandwich two viscous fluid films as shown in the figure. Thetop plate moves with a velocity of 1.5 m/s and the lower plate is free to move under the influenceof the viscous force applied to it. The contact areas for the lower surface of the upper plate is thesame as the upper surface of the lower plate as well as the lower surface of lower plate and thatof the fixed surface. The density of both fluid is 850 kg/m3. hı=2 mm, hz=1 mm, µi=0.2 Pas.u2=0.5 Pas.(a) After steady state conditions have been reached, what is the velocity of the lower plate?(b) What is the force per unit area imposed on the upper plate to maintain its velocity?Upper plateViscous fluid 1h1Lower plateViscous fluid 2h2Fixed surface.3. Unsteady flow between two infinite plates. The upper plate (y-h) is fixed; at time t=0, thelower plate (y=0) begins to move at uniform velocity Uo. Starting from governing equations forparallel flow and list all assumptions, solve the unsteady PDE by separation of variables.4. Given laminar fully developed flow in an elliptical duct of şemiaxes a and b. Show that, for agiven pressure gradient, the flow rate per unit area is a maximum when a=b. 1. Answer the following questions:(a) What is the physical meaning of the following:D aDtwhere V is the velocity vector of the flow field.(b) Let the viscous stress tensor be denoted by 7. How is the surface (vector) force f, acting bythe fluid on a surface element ds (with unit normal în ) computed? Give your answer in vectornotation and also in index notation. What is the physical meaning of tyy ?(c) Write down the work done on a material volume of fluid by the viscous surface force invector notation and also in index notation.(d) Write down the amount of conduction heat flux 'q' (a scalar) on a surface element ds (withunit normal în ) in vector notation and also in index notation.2. Two plates and a fixed surface sandwich two viscous fluid films as shown in the figure. Thetop plate moves with a velocity of 1.5 m/s and the lower plate is free to move under the influenceof the viscous force applied to it. The contact areas for the lower surface of the upper plate is thesame as the upper surface of the lower plate as well as the lower surface of lower plate and thatof the fixed surface. The density of both fluid is 850 kg/m3. hı=2 mm, hz=1 mm, µi=0.2 Pas.u2=0.5 Pas.(a) After steady state conditions have been reached, what is the velocity of the lower plate?(b) What is the force per unit area imposed on the upper plate to maintain its velocity?Upper plateViscous fluid 1h1Lower plateViscous fluid 2h2Fixed surface.3. Unsteady flow between two infinite plates. The upper plate (y-h) is fixed; at time t=0, thelower plate (y=0) begins to move at uniform velocity Uo. Starting from governing equations forparallel flow and list all assumptions, solve the unsteady PDE by separation of variables.4. Given laminar fully developed flow in an elliptical duct of şemiaxes a and b. Show that, for agiven pressure gradient, the flow rate per unit area is a maximum when a=b.

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Given laminar fully developed flow in an elliptical duct of semiaxes a and b. Show that, for a given pressure gradient, the flow rate per unit area is a maximum when a=b.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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