? % H2SO4 ?%HNO3 7%H2O ? % HNO3 ?%H20 ? % H2SO4 7%H20 A D 1000 lb ? % H2SO4 ?%HNO3

Back HW#2 QUESTION1/60pts] A fluid of viscosity u flows in the horizontal cylinder (radius R) shown in the figure under a constant pressure gradient dP/dx. The inner core of the cylinder is filled with a porous material. The flow in this porous region is slow and assumed to be a plug-type flow such that the velocity is constant and everywhere the same inside the porous region. Denote this velocity by Uo. The flow in the open (non-porous) region is steady, Newtonian, incompressible and axisymmetric. It will be assumed that only the axial (x) component of the velocity is non-zero. Flow Open flow T&R Porous media flow R N.B. All your answers must be expressed in terms of µ, U₁, a, R and dP/dx. (a) Use the continuity and Navier-Stokes equations to determine the expression of the velocity in the open region. (b) What is the expression of the average velocity in the open region? (c) Is the assumption of a linear velocity profile in the open region acceptable when this region Tuatifi 1:

Experiments conducted for a dilute system under laboratory conditions approximating plug flow give HTUOx= 3 ft. If a commercial column is to be designed for NTUOx = 4, with NPex and NPey estimated to be 19 and 50, respectively, determine the necessary column height if E = 0.5.

HOMEWORK-2 Considering the steady-state laminar flow of a liquid with density p and viscosity p in a vertical tube of length L and radius R; a) Show the momentum flux and velocity profile in the figure. b) Determine the momentum flux distribution, the velocity distribution, the maximum velocity (Vzmax), and the average velocity (Vzaverage) expressions. PL L R ! Po 1111111 Flow in

What do you mean by volumetric flow rate?

fluid flow between parallel plates (Fig. 2) that are horizontal and a distance 2h apart. A constant pressure gradient is applied in the x-direction (dp/dx). The flow is fully developed laminar and steady. The plate width is denoted by B a) Simplify the governing equations b) Define the boundary conditions c) Determine the velocity profile d) Develop an expression for the flow rate Continuity Equation ap d + at əx Momentum Equations d'u dr P8x P8y P8z ə a (pu) + (pv) + (pw) = 0 dy əz др Əx + μ әр + м ду ap + M əz d²v dx² + azu dy d²v dy² + + d²u az² ²v əz² a²w dz² azw dzw + + ay² dx² www. p P ди Ət dv at aw at + u + u + u ди ax dv əx dw ax y + v + v g Fixed Fig. 2: Flow between parallel plates with a co- pressure gradient ди + v ду dv ду + w aw ду + W ди az dv + w əz dw u(y) əz #max 介介