A laminar flow of constant density and constant viscosity at steady state flows thought the two...
Water is in steady fully developed laminar flow between two horizontal, very wide (W) and long (L) parallel surfaces separated by a distance b. The bottom surface at y 0 moves in the negative x-direction at a speed vo while the top surface at y b is stationary. In addition, a constant pressure gradient dP/dx is acting on the liquid in the x-direction. (a) Write the simplified form of the Navier-Stokes equation and the appropriate boundary conditions. (b) Derive an...
1. As seenfrom figure, there is a laminar and viscous fluid flow betweentwo parallel plates where the one is moving with velocity y, other one is stationary. There exists pressure gradient in x direction. The bottom stationary plate is a porous plate andfluid is injected into the channel with V velocity. If theflow is steady, fully developed and incompressible flow, derive the velocity profile. Uo Vo 1. As seenfrom figure, there is a laminar and viscous fluid flow betweentwo parallel...
fluid mechanics A steady, incompressible, and laminar flow of a fluid of viscosity u flows through an inclined narrow gap of a crack in the wall of length L and a constant width W shown in Figure Q1(b). Assume that the gap has a constant thickness of 7. The fluid flows down the inclined gap at an angle and in the positive x-direction. No pressure gradient is applied throughout the flow but there is gravitational effect. Derive an expression for...
2. Consider a polymer (with density p and viscosity u) flowing in between two parallel plates in a vertical position. Both plates are stationary at x = 0 and x = h. A downward pressure is applied - dp/dz which is constant across the z-direction, which is also aided by gravity acting on the negative z-direction. Starting with the Navier-Stokes equations, find the simplified equation that defines the fluid velocity vz. State your assumptions to achieve this simplified equation. (7pts)...
Problem 5. Consider a (i) steady, (ii) incompressible, axisymmetric, (iv) fully- developed, (v) constant viscosity, (vi) laminar flow in a circular pipe. Assume that the pipe is horizontal, so that any gravitational effects can be ignored It is known that an incompressible, constant viscosity fluid can be described by the continuity equation in cylindrical coordinates together with the Naiver-Stokes equations (ak.a., momentum eqns) in cylindrical coor- dinates Ov 00. Or 9-moment um 11ap 2-momentum plus the appropriate boundary conditions. Starting...
3. (20 pts) A constant-thickness film of viscous liquid flows in laminar motion down a plate inclined at an angle 6, as shown in the figure. The velocity profile is (a) Find the constant C in terms of the specific weight and viscosity and the angle θ. Find the volume flux O per unit width in terms of these parameters. (b) What are the appropriate boundary conditions at y 0 and y h? uly) 3. (20 pts) A constant-thickness film...
Consider the case of a Newtonian fluid undergoing laminar, pressure-driven flow between two parallel, infinite flat plates separated by a distance B (Figure). The bottom plate is stationary and the top plate moves at a constant velocity Vup. For a constant dynamic pressure gradient, AP/AX, P-p-g r, we wish to calculate the resulting velocity profile. 9--(%) + mai Differentiation equation: B.C.v. (y=0) -0,vxly - B) - Vu Figure 1.10 Pressure-driven flow between two infinite, parallel, flat plates. (i) () Use...
An incompressible fluid flows between two porous, parallel flat plates as shown in the Figure below. An identical fluid is injected at a constant speed V through the bottom plate and simultaneously extracted from the upper plate at the same velocity. There is no gravity force in x and y directions (g-g,-0). Assume the flow to be steady, fully-developed, 2D, and the pressure gradient in the x direction to be a constant P = constant). (a) Write the continuity equation...
Problem 3- For flow of an incompressible, Newtonian fluids between parallel plates, the velocity distribution between the plate is given by 1 dP 2μ dr where y is the direction from one plate (y-0) to another (y-w),and x is the direction of flow a) What is the expression for the rate of deformation matrix? b) What is the expression for the stress matrix? c) At the center of the flow y w/2, what is the direction of internal forcing due...
Consider the steady, laminar flow of two liquids, A and B, with viscosities HA-μ and μΒ 21, respectively, between infinite parallel plates at 2- a, as shown in the diagram below. The plate at 2 a is fixed, while the plate at 2a moves with constant velocity -Vi, where V0. The liquids do not mix, and each forms a layer of depth a. There is an applied pressure gradient acting on both liquids, given by ▽p--Ci (where C > 0...