A fluid is bounded by two parallel plates of infinite width and length as shown in FIGURE Q1. The upper plate moves at 7 m/s, and the lower plate is fixed. The fluid's dynamic viscosity is 1.85X10-5 N.s/m². Assume Couette flow with pressure gradient, = 0.1 N/m³. a. Propose the discretization method to solve Couette flow equation with pressure gradient below. Let the number of nodes, n = 9, the distance between the nodes is 0.05 m. Obtain the velocity of all the internal nodes using the matrix inversion method and the iterative method. Compare the results and the effectiveness of both methods (in terms of calculation effort and ease of setting up the problem). 0= b. Flow shear stress is governed by the following equation du t=μ= Propose the discretization method to solve the above equation and calculate the shear stress at node 1. Describe the condition in terms of the pressure gradient when the shear stress at the bottom plate is zero.

A fluid is bounded by two parallel plates of infinite width and length as shown in FIGURE Q1. The upper plate moves at 7 m/s, and the lower plate is fixed. The fluid's dynamic viscosity is 1.85X10-5 N.s/m². Assume Couette flow with pressure gradient, = 0.1 N/m³. a. Propose the discretization method to solve Couette flow equation with pressure gradient below. Let the number of nodes, n = 9, the distance between the nodes is 0.05 m. Obtain the velocity of all the internal nodes using the matrix inversion method and the iterative method. Compare the results and the effectiveness of both methods (in terms of calculation effort and ease of setting up the problem). 0= b. Flow shear stress is governed by the following equation du t=μ= Propose the discretization method to solve the above equation and calculate the shear stress at node 1. Describe the condition in terms of the pressure gradient when the shear stress at the bottom plate is zero.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

1) The velocity profile of a viscus fluid over a plate is parabolie with vertex 25 em from the plate ,where the velocity 125 cm/s. calculate the velocity gradient and shear stress at distance of (0, 5, 15 and 25 cm) from the plate given the viscosity of the fluid =7 poise ? Also draw the figure explain the relationship between the velocity gradient and shear stress. Take velocity profile for parabolic equation, (v = ay + by + c)
is called a cone-plate viscometer A solid cone of angle 2k, base 1, and density p, is rotat- Ing with initial angular velocity my inside a conical.seat, as shown in Fig. of viscosity u. Neglecting air drag, derive an analytical ex- pression for the cone's angular velocity ) if there is no applied tongue. The device in Fig. The angle of the cone is very small, so thiat sin 0 0, and the gap is filled with the test liquid. The torque M to rotate the cone at a rate 1 is measured. Assuming a lin- ear velocity profile in the fluid film, derive an expression for tiuid viscosity u as a tumction of (M, R. S2, 0). The clearance h is filled with nil Bave C co radius a dwit) dt Fluid I manmot 1Inentia Derive an expression for the capillary height change h for a fluid of surface tension Y and contact angle 0 between two vertical parallel plates a distance W apart, as in Fig. . What will li be for water at 20°C if W = 0.5 mm? A thin plate is separated from two fixed plates by very vis- cous liquids…
Asap
Under laminar conditions, the volume flow Q through asmall triangular-section pore of side length b and length Lis a function of viscosity μ , pressure drop per unit length∆p / L , and b . Using the pi theorem, rewrite this relation indimensionless form. How does the volume flow change ifthe pore size b is doubled?
Derive the Bernoulli's Equation from the navier stoke's equation. Considering - no viscosity - incompressible fluid(constant density) - steady flow (constant velocity)
A viscous incompressible Newtonian fluid is contained between two fixed parallel plates inclined at an angle 0, and the flow is driven by both constant pressure gradient E = constant) and gravity. The distance between the two plates is 2H and the chosen system of coordinates is shown in the figure. Assuming steady, 2D, and parallel flow (v = w = 0) and using differential analysis: (a) Show that the flow is fully developed using continuity equation; and (b) Find the velocity profile u(y) in terms of ,H,P,g,0,H de using Navier-Stokes equations with appropriate boundary conditions. 211
Take the full-blown Couette flow as shown in the figure. While the upper plate is moving and the Lower Plate is constant, flow occurs between two infinitely parallel plates separated by the H distance. The flow is constant, uncompressed, and two-dimensional in the X-Y plane. In fluid viscosity µ, top plate velocity V, distance h, fluid density ρ, and distance y, create a dimensionless relationship for component X of fluid velocity using the method of repeating variables. Show all steps in order.
A cubic block of side L and mass M is dragged over an oil film across table by a string connects to a hanging block of massmas shown in figure. The Newtonian oil film of thickness h has dynamic viscosity u and the flow condition is laminar. The acceleration due to gravity is g. The steady state velocity V of block is M Mgh (a) Mgh (b) mgh (c) mgh (d)
An infinite plate is moved over a second plate on a layer of liquid as shown. For small gap width, d, we assume a linear velocity distribution in the liquid. The liquid kinematic viscosity is 0.00739 cm²/s and its density is 880 kg/m³. Determine the shear stress on the upper plate, in N/m?. y U = 0.3 m/s d = 0.3 mm
An incompressible fluid (kinematic viscosity, 7.4 x10-7 m²/s, specific gravity, 0.88) is held between two parallel plates. If the top plate is moved with a velocity of 0.5 m/s while the bottom one is held stationary, the fluid attains a linear velocity profile in the gap of 0.5 mm between these plates; the shear stress in Pascals on the surface of top plate is rt of this book may be repro
The laminar flow of a fluid with a constant viscosity, 4, inside a channel is governed by the following boundary value problem (strong form): d'u dp for y E (0, h) "dy dr u = 0 at y = 0 and y = h vhere u is the fluid velocity and is the pressure drop in the direction of the flow. a) Derive the weak form of the boundary value problem described above.
A cube of side (a) and mass (M) is initially sitting fully submerged at the bottom of a container filled with a liquid of kinematic viscosity v and density p. The container has a square cross-section of side (a+a/5) and the cube is sitting right at the middle of the container base. (a) A force (F) starts pulling the cube up at a constant velocity (U). Develop an expression for the force in terms of (U, M. a. g, p and v). You may assume that the velocity in the gap between the cube's sides and the container walls is linear. The expression for (F) is to be valid as long as the cube remains submerged. (b) After the cube reaches the water surface, it continues to be pulled up by the same force. Develop a differential equation for the variation with time of the fraction of the cube that is submerged in water.