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Task 9 4 Pts A flow of two layers of immiscible liquids is flowing through a...
Task 8 6 Pts A so called "flow straightener" is arranged in a tube to produce...
Task 8 6 Pts A so called "flow straightener" is arranged in a tube to produce a flat velocity profile, independent of the profile which is created by the flow. The straightener consist of a package of parallel-arranged thin tubes with small inner diameter, which fills out the entire cross section of the hosting tube (see fig. 1). Here a special design of the straightener is used: it consists of 50 tubes with quadratic cross section (0.025 0.025 m²) and...
Consider the steady, laminar flow of two liquids, A and B, with viscosities HA-μ and μΒ...
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...
Water is in steady fully developed laminar flow between two horizontal, very wide (W) and long...
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...
HW 8 Poiseuille flow: Fully developed laminar pipe flow (in cylindrical coordinate) - The simplified z-momentum...
HW 8 Poiseuille flow: Fully developed laminar pipe flow (in cylindrical coordinate) - The simplified z-momentum equation - The boundary conditions = No slip at r=R The Navier-Stokes equation for 2D (x,y) incompressible flow DV P -Op+uv2V + pg dt - Assumptions: 1. 2. 3. 4. 5. 6. Finite velocity at r=0 - Final velocity solution of Poiseuille flow - The rz component of the NS equation (in cylindrical coordinate) - Volume flow rate (Q = ſ vedA)
An important problem in chemical engineering separation equipment involves thin liquid films flow...
An important problem in chemical engineering separation equipment involves thin liquid films flowing down vertical walls due to gravity, as shown in this figure yV A. Assume that the wall is long and wide compared to the film thickness, with steady flow that is laminar and fully developed: u= v=0 and w w(x). Using a force balance on a rectangular differential element, derive an expression relating g, p, and τΧΖ . Use τΧΖ-n(-_ +--) for a Newtonian fluid to convert...
An important problem in chemical engineering separation equipment involves thin liquid films flowing down vertical walls...
An important problem in chemical engineering separation equipment involves thin liquid films flowing down vertical walls due to gravity, as shown in this figure yV A. Assume that the wall is long and wide compared to the film thickness, with steady flow that is laminar and fully developed: u= v=0 and w w(x). Using a force balance on a rectangular differential element, derive an expression relating g, p, and τΧΖ . Use τΧΖ-n(-_ +--) for a Newtonian fluid to convert...
PROBLEM 1: Answer/Define/Explain shortly and/or Fill in the blanks (40 P) a) What are the two...
PROBLEM 1: Answer/Define/Explain shortly and/or Fill in the blanks (40 P) a) What are the two types of energy transfer in Convection? b) A thermal boundary layer must develop if ....... c) Define the critical Reynolds number. d) What are the assumptions for Boundary Layer Equations for Laminar Flow? e) Define the Nusselt number. f) Define the Prandtl number. g) How the Pr influences the relative growth of the boundary layers, explain briefly ? h) Explain favorable pressure gradient. i)...
2- (40 pts) Using Navier-Stokes equations, in class we developed the velocity profile between two stationary...
2- (40 pts) Using Navier-Stokes equations, in class we developed the velocity profile between two stationary infinite parallel plates for a laminar, fully developed, steady flow. Here is the exact same flow: u(y) = 2 ( 0) (02 – hy) v= 0 a) Find the expression for average velocity for such flow. b) Use the average velocity you calculated in (a) to find the expression for volume flow rate per unit width into the page. c) If at x=105 m...
Two horizontal plates with infinite length and width are separated by a distance H in the...
Two horizontal plates with infinite length and width are separated by a distance H in the zdirection. The bottom plate is moving at a velocity vx=U. The incompressible fluid trapped between the plates is moving in the positive x-direction with the bottom plate. Align gravity with positive z. Assume that the flow is fully-developed and laminar. If the systems operates at steady state and the pressure gradient in x-direction can be ignored, do the following: 1. Sketch your system. 2....
Task 8 6 Pts A so called "flow straightener" is arranged in a tube to produce a flat velocity profile, independent of the profile which is created by the flow. The straightener consist of a package of parallel-arranged thin tubes with small inner diameter, which fills out the entire cross section of the hosting tube (see fig. 1). Here a special design of the straightener is used: it consists of 50 tubes with quadratic cross section (0.025 0.025 m²) and...
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...
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...
HW 8 Poiseuille flow: Fully developed laminar pipe flow (in cylindrical coordinate) - The simplified z-momentum equation - The boundary conditions = No slip at r=R The Navier-Stokes equation for 2D (x,y) incompressible flow DV P -Op+uv2V + pg dt - Assumptions: 1. 2. 3. 4. 5. 6. Finite velocity at r=0 - Final velocity solution of Poiseuille flow - The rz component of the NS equation (in cylindrical coordinate) - Volume flow rate (Q = ſ vedA)
An important problem in chemical engineering separation equipment involves thin liquid films flowing down vertical walls due to gravity, as shown in this figure yV A. Assume that the wall is long and wide compared to the film thickness, with steady flow that is laminar and fully developed: u= v=0 and w w(x). Using a force balance on a rectangular differential element, derive an expression relating g, p, and τΧΖ . Use τΧΖ-n(-_ +--) for a Newtonian fluid to convert...
An important problem in chemical engineering separation equipment involves thin liquid films flowing down vertical walls due to gravity, as shown in this figure yV A. Assume that the wall is long and wide compared to the film thickness, with steady flow that is laminar and fully developed: u= v=0 and w w(x). Using a force balance on a rectangular differential element, derive an expression relating g, p, and τΧΖ . Use τΧΖ-n(-_ +--) for a Newtonian fluid to convert...
PROBLEM 1: Answer/Define/Explain shortly and/or Fill in the blanks (40 P) a) What are the two types of energy transfer in Convection? b) A thermal boundary layer must develop if ....... c) Define the critical Reynolds number. d) What are the assumptions for Boundary Layer Equations for Laminar Flow? e) Define the Nusselt number. f) Define the Prandtl number. g) How the Pr influences the relative growth of the boundary layers, explain briefly ? h) Explain favorable pressure gradient. i)...
2- (40 pts) Using Navier-Stokes equations, in class we developed the velocity profile between two stationary infinite parallel plates for a laminar, fully developed, steady flow. Here is the exact same flow: u(y) = 2 ( 0) (02 – hy) v= 0 a) Find the expression for average velocity for such flow. b) Use the average velocity you calculated in (a) to find the expression for volume flow rate per unit width into the page. c) If at x=105 m...
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