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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 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...
12. A liquid flows in a slit in the z-direction down a vertical plane, between 2...
12. A liquid flows in a slit in the z-direction down a vertical plane, between 2 broad parallel plates with distance L under the influence of gravity,g, with the plane parallel to the axis of gravity. Assume a uniform thickness of 2D for the liquid layer in the x-direction, steady state laminar flow, and that the fluid is Newtonian and incompressible. The plate at x=0 is heated to a constant temperature of Tp and all the fluid enters the slit...
A. In the table below, identify which of the circled terms of the governing equations can...
A. In the table below, identify which of the circled terms of
the governing equations can be neglected
by the given assumption. Write the number of the term in the table.
Some assumptions relate
to multiple terms, include them all.
B. Write the mathematical equations describing the
appropriate boundary conditions and identify
them in words.
C. Applying the appropriate boundary conditions,
solve the differential equation remaining after
appropriate terms have been neglected to determine the velocity
profile in the film: d^2(w)/dx^2 =...
Problem 1: Differential Relations for a Fluid Particle (25 points) Two horizontal, infinite, parallel plates are...
Problem 1: Differential Relations for a Fluid Particle (25 points) Two horizontal, infinite, parallel plates are spaced a distance b apart. A viscous liquid is contained between the plates. The bottom plate is fixed, and the upper plate moves parallel to the bottom plate with a velocity U. Assume no-slip boundary conditions. There is no pressure gradient in the direction of flow (a) Demonstrate using the Navier-Stokes equation in the x-direction that the velocity profile is of the form: (15...
1. Fluid between parallel plates down an inclined plane (gravity setler). Fluid is flowing between parallel...
1. Fluid between parallel plates down an inclined plane (gravity setler). Fluid is flowing between parallel plates, at an angle of β to the vertical. Assume δ<<w, L. th a momentum balance on a differential shell, and using the notation shown below, derive: i. the velocity distribution in the fluid, v,-f(x/b), and sketch result ii. the shear stress distribution in the fluid, -f(x/ö), and sketch result. iii. the volumetric flow rate iv. the maximum velocity, and the position x where...
19 A vertical moving belt drags an incompressible liquid film of thickness h, density P, and...
19 A vertical moving belt drags an incompressible liquid film of thickness h, density P, and viscosity , as shown. Gravity tends to make the liquid drain down, but the movement of the belt at speed U, keeps the liquid from running off completely. u Assume that the flow is full developed and stead. State the boundary conditions Write the continuity equation for the flow and solve for v, the horizontal component of velocity. Solve for the velocity profile u(y)...
please solve all parts and show all steps especially parts b) and d) Problem (3) 140...
please solve all parts and show all steps
especially parts b) and d)
Problem (3) 140 pointsl Consider a viscous film of liquid draining uniformly down the side of a vertical rod or radius (a) and length of (L), as shown in figure. Assume that the atmosphere offers no shear resistance to the film motion and the flow is axi-symmetry. Determine the following a) Show that , ,(r) only. b) Verify o. c) Derive the differential equation for v,, state...
hi i am in a fluid dynamics class and need some help with the question attached....
hi i am in a fluid dynamics class and need some help with the
question attached. please be specific and write out all steps so i
know how to do the problem.
A belt moves upward at velocity V, dragging a film of viscous liquid of constant thickness h. Near the belt, the film moves upward due to no slip. At its outer edge, the film moves downward due to gravity. - liquid dynamic viscosity: u density:P belt 1- Using...
Problem 3: In a molten-salt nuclear reactor, radioactive liquid is flowing through a cylindrical pipe of diameter D. Fi...
Problem 3: In a molten-salt nuclear reactor, radioactive liquid is flowing through a cylindrical pipe of diameter D. Fission in the liquid results in a uniform internal heat generation of à W/m3. The pipe wall also has a heater on it that can provide a uniform surface heating rate of q" W/m2. The radioactive liquid has a specific heat capacity of Cp J/kg-K, a mass flowrate of m kg/s, and an inlet temperature of Tm, Conduction in the fluid in...
Consider the steady, incompressible flow of depth h of a liquid of known density ρ and...
Consider the steady, incompressible flow of depth h of a liquid
of known density ρ and unknown viscosity µ down a flat plate as
shown in Figure 1. Air is the fluid above the liquid layer. The
force of gravity is in the vertical direction with acceleration g,
and the plate is at an angle θ with respect to the horizontal.
Assuming the coordinate system as shown, with x aligned with the
flow direction, and y normal to the plate,...
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...
12. A liquid flows in a slit in the z-direction down a vertical plane, between 2 broad parallel plates with distance L under the influence of gravity,g, with the plane parallel to the axis of gravity. Assume a uniform thickness of 2D for the liquid layer in the x-direction, steady state laminar flow, and that the fluid is Newtonian and incompressible. The plate at x=0 is heated to a constant temperature of Tp and all the fluid enters the slit...
A. In the table below, identify which of the circled terms of
the governing equations can be neglected
by the given assumption. Write the number of the term in the table.
Some assumptions relate
to multiple terms, include them all.
B. Write the mathematical equations describing the
appropriate boundary conditions and identify
them in words.
C. Applying the appropriate boundary conditions,
solve the differential equation remaining after
appropriate terms have been neglected to determine the velocity
profile in the film: d^2(w)/dx^2 =...
Problem 1: Differential Relations for a Fluid Particle (25 points) Two horizontal, infinite, parallel plates are spaced a distance b apart. A viscous liquid is contained between the plates. The bottom plate is fixed, and the upper plate moves parallel to the bottom plate with a velocity U. Assume no-slip boundary conditions. There is no pressure gradient in the direction of flow (a) Demonstrate using the Navier-Stokes equation in the x-direction that the velocity profile is of the form: (15...
1. Fluid between parallel plates down an inclined plane (gravity setler). Fluid is flowing between parallel plates, at an angle of β to the vertical. Assume δ<<w, L. th a momentum balance on a differential shell, and using the notation shown below, derive: i. the velocity distribution in the fluid, v,-f(x/b), and sketch result ii. the shear stress distribution in the fluid, -f(x/ö), and sketch result. iii. the volumetric flow rate iv. the maximum velocity, and the position x where...
19 A vertical moving belt drags an incompressible liquid film of thickness h, density P, and viscosity , as shown. Gravity tends to make the liquid drain down, but the movement of the belt at speed U, keeps the liquid from running off completely. u Assume that the flow is full developed and stead. State the boundary conditions Write the continuity equation for the flow and solve for v, the horizontal component of velocity. Solve for the velocity profile u(y)...
please solve all parts and show all steps
especially parts b) and d)
Problem (3) 140 pointsl Consider a viscous film of liquid draining uniformly down the side of a vertical rod or radius (a) and length of (L), as shown in figure. Assume that the atmosphere offers no shear resistance to the film motion and the flow is axi-symmetry. Determine the following a) Show that , ,(r) only. b) Verify o. c) Derive the differential equation for v,, state...
hi i am in a fluid dynamics class and need some help with the
question attached. please be specific and write out all steps so i
know how to do the problem.
A belt moves upward at velocity V, dragging a film of viscous liquid of constant thickness h. Near the belt, the film moves upward due to no slip. At its outer edge, the film moves downward due to gravity. - liquid dynamic viscosity: u density:P belt 1- Using...
Problem 3: In a molten-salt nuclear reactor, radioactive liquid is flowing through a cylindrical pipe of diameter D. Fission in the liquid results in a uniform internal heat generation of à W/m3. The pipe wall also has a heater on it that can provide a uniform surface heating rate of q" W/m2. The radioactive liquid has a specific heat capacity of Cp J/kg-K, a mass flowrate of m kg/s, and an inlet temperature of Tm, Conduction in the fluid in...
Consider the steady, incompressible flow of depth h of a liquid
of known density ρ and unknown viscosity µ down a flat plate as
shown in Figure 1. Air is the fluid above the liquid layer. The
force of gravity is in the vertical direction with acceleration g,
and the plate is at an angle θ with respect to the horizontal.
Assuming the coordinate system as shown, with x aligned with the
flow direction, and y normal to the plate,...
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