Question 2 Given a steady, incompressible, laminar flow of a Newtonian fluid in the narrow gap between two infinite para

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Question 2 Given A Steady Incompressible Laminar Flow Of A Newtonian Fluid In The Narrow Gap Between Two Infinite Para 1 (72.77 KiB) Viewed 13 times

Question 2 Given A Steady Incompressible Laminar Flow Of A Newtonian Fluid In The Narrow Gap Between Two Infinite Para 2 (40.91 KiB) Viewed 13 times

Question 2 Given a steady, incompressible, laminar flow of a Newtonian fluid in the narrow gap between two infinite parallel plates as in Figure 1. The top plate is moving at speed V, and the bottom plate is stationary. The distance between these two plates is h, and gravity acts in the negative z-direction into the page in Figure 1). There is no applied pressure other than hydrostatic pressure due to gravity. This flow is called Couette flow. (Diberi satu bendalir Newtonian yang mantap, tak boleh mampat, aliran lamina dalam satu sela sempit diantara dua plat selari yang tidak terhingga panjangnya sepertimana yang ditunjukkan dalam Gambarajah 1. Plat atas bergerak dengan halaju V dan plat bawah adalah pegun. Jarak diantara dua plat itu adalah h, dan gravity bertindak pada negatif arah-- (menghala kedalam mukasurat Gambarajah 1). Tiada sebarang tekanan dikenakan selain dari tekanan hidrostatik yang disebabkan oleh gravity. Aliran ini dinamakan aliran Couette.) Assumptions: [Andaian:) i. The length of the plates are infinite in the x and a direction. [Panjang plat adalah tak terhingga dalam arah x dan z] ii. The flow is steady. (Aliran adalah mantap. iii. This is a parallel flow. [Ini adalah alilran selari.] iv. The fluid is incompressible and Newtonian with constant properties, and the flow is laminar. (Bendalir adalah tak boleh mampat dan Newtonian dengan sifat-sifat pemalar, dan aliran adalah lamina. v. Pressure P=constant with respect to x direction. (Tekanan P-pemalar pada arah x] vi. The velocity field is purely two-dimensional. [Medan halaju adalah dua dimensi semata-mata.) vii. Gravity acts in the negative z-direction (into the page of Figure 1). (Graviti bertindak pada arah z negatif (kedalam mukasurat Gambarajah 1)] (a) Simplify the differential equation of the incompressible continuity equation in Cartesian coordinates according to the above assumption. [Berdasarkan kepada andalan diatas, ringkaskan persamaan kebezaan untuk persamaan keterusan tak boleh mampat didalam koordinat Cartesian] (2 Marks / Markah)
(b) Simplify the incompressible Navier-Stokes equation of x,y and a direction according to the above assumption. (Berdasarkan kepada andaian diatas, ringkaskan persamaan persamaan Navier-Stokes tak boleh mampatuntuk arah x, y danz.) (4 Marks / Markah) c) Determine the velocity and pressure fields of the fluid. Tentukan medan halaju dan tekanan bendalir tersebut.) (6 Marks / Markah) (d) Sketch the result of velocity profile of the fluid in between those two plates. [Lakarkan susuk keputusan halaju bendalir yang terhasil diantara dua plat tersebut. (2 Marks/Markah) (e) Estimate the shear force per unit area acting on the bottom plate. Anggarkan tegasan ricih daya per unit luas yang bertindak diatas plat bawah.) (6 Marks/Markah) Moving plate Fluid: pH Fixed plate Figure 1 (Gambarajah 1) XX IS A fully developed region of a flow field is a region where the velocity profile does not change with downstream distance. Fully developed flows are encountered in long, straight channels and pipes. Fully developed Couette flow is shown here-the velocity profile at xs is identical to that at Xx.