Two immiscible Newtonian fluids are contained between infinite parallel plates. The plates are separated by distance...
Two immiscible Newtonian fluids are contained between infinite parallel plates. The plates are separated by distance 4h, and the top fluid layer thickness is h. The bottom layer has thickness 3h. The viscosity of the bottom fluid is three times that of the top fluid. If the lower plate moves at a constant speed of 20 m/s and the upper plate moves at a constant speed of 40 m/s, what is the average velocity within the bottom liquid layer? We assume steady state.
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Two immiscible Newtonian fluids are contained between infinite
parallel plates. The plates are separated by distance...
10. Immiscible fluids Two immiscible incompressible Newtonian fluids flow together through in thedirection two lates separated...
10. Immiscible fluids Two immiscible incompressible Newtonian fluids flow together through in thedirection two lates separated by a distance H in the y-direction. Let us make thé top plate /move with ection while fixing the bottom plate. At steady state, however, there be a little slip velocity of the more dense fluid only at the lower boundary The flow constant vetocity V in the x-dir is ynidirectional and faminar. For convenience, we take that x is the flow direction and...
A Newtonian body wash undergoes steady shear between two horizontal parallel plates. The lower plate is...
A Newtonian body wash undergoes steady shear between two horizontal parallel plates. The lower plate is fixed, and the upper plate of 1kg moves with constant velocity of 20 m/s. The distance between the plates is constant at 5 mm. The area of the upper plate in contact with the fluid is 0.5 m2 . a) What is the viscosity of the product and b) the momentum diffusivity if its density is 1010 kg/m3?
4. Consider fully developed Couette flow-flow between two infinite parallel plates separated by distance h, with...
4. Consider fully developed Couette flow-flow between two infinite parallel plates separated by distance h, with the top plate moving and the bottom plate stationary. The flow is steady, incompressible, and two-dimensional in the xy- plane. Use the method of repeating variables to generate a dimensionless relationship for the x component of fluid velocity u as a function of fluid viscosity , top plate speed V, distance h, fluid density p, and distance y Show all your work. Hint: u...
Consider steady, incompressible, laminar flow of a Newtonian fluid in the narrow gap between two infinite...
Consider steady, incompressible, laminar flow of a Newtonian fluid in the narrow gap between two infinite parallel plates. The top plate is moving at speed V, and the bottom plate is moving in the opposite direction at speed V. The distance between these two plates is h, and gravity acts in the negative z-direction. There is no applied pressure other than hydrostatic pressure due to gravity. Calculate the velocity and estimate the shear stress acting on the bottom plate Moving...
2.22. Three parallel flat plates are separated by two fluids. Plate 1 (on the bottom) is...
2.22. Three parallel flat plates are separated by two fluids. Plate 1 (on the bottom) is at rest. Water, viscosity 0.8007 CP at 30°C, lies between plates 1 and 2. Toluene, viscosity 0.5179 cP at 30°C, lies between plates 2 and 3. The distance between each pair of plates is 10 cm. Plate 3 moves at 3 ms. Find: (a) the velocity of plate 2 at steady-state (b) the force per unit area on plate 3 required to maintain the...
Problem 3- For flow of an incompressible, Newtonian fluids between parallel plates, the velocity ...
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 case of a Newtonian fluid undergoing laminar, pressure-driven flow between two parallel, infinite flat...
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...
A fluid having a viscosity u 9.35 x 104 lbf-s/ft is contained between two parallel plates,...
A fluid having a viscosity u 9.35 x 104 lbf-s/ft is contained between two parallel plates, each of which has a cross section of 200 in2. The bottom plate is fixed whereas the top plate moves at a constant velocity of 4 ft/s when a shearing force is applied. The separation distance between the plates is a uniform 0.05 in. Assume the velocity distribution in the fluid is linear. Determine the following: 4. the shear stress in the fluid (lbf/in2)...
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...
fluids of varied viscosities between two plates
Fluids ofviscosities μ1 = .15 N*s/m^2, μ2 = 0.5 Ns/m^2, μ3 = 0.2 Ns/m^2 are contained between two parallel plates (each plate is 1 m^2 in area). Thethicknesses are h1 = 0.5mm, h2 = 0.25mm, h3 0.2mm. Find the steady speed V of the upper plate and the velocities at the two interfaces due to a force F = 100N.Plot the velocity distribution.
10. Immiscible fluids Two immiscible incompressible Newtonian fluids flow together through in thedirection two lates separated by a distance H in the y-direction. Let us make thé top plate /move with ection while fixing the bottom plate. At steady state, however, there be a little slip velocity of the more dense fluid only at the lower boundary The flow constant vetocity V in the x-dir is ynidirectional and faminar. For convenience, we take that x is the flow direction and...
4. Consider fully developed Couette flow-flow between two infinite parallel plates separated by distance h, with the top plate moving and the bottom plate stationary. The flow is steady, incompressible, and two-dimensional in the xy- plane. Use the method of repeating variables to generate a dimensionless relationship for the x component of fluid velocity u as a function of fluid viscosity , top plate speed V, distance h, fluid density p, and distance y Show all your work. Hint: u...
Consider steady, incompressible, laminar flow of a Newtonian fluid in the narrow gap between two infinite parallel plates. The top plate is moving at speed V, and the bottom plate is moving in the opposite direction at speed V. The distance between these two plates is h, and gravity acts in the negative z-direction. There is no applied pressure other than hydrostatic pressure due to gravity. Calculate the velocity and estimate the shear stress acting on the bottom plate Moving...
2.22. Three parallel flat plates are separated by two fluids. Plate 1 (on the bottom) is at rest. Water, viscosity 0.8007 CP at 30°C, lies between plates 1 and 2. Toluene, viscosity 0.5179 cP at 30°C, lies between plates 2 and 3. The distance between each pair of plates is 10 cm. Plate 3 moves at 3 ms. Find: (a) the velocity of plate 2 at steady-state (b) the force per unit area on plate 3 required to maintain the...
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 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...
A fluid having a viscosity u 9.35 x 104 lbf-s/ft is contained between two parallel plates, each of which has a cross section of 200 in2. The bottom plate is fixed whereas the top plate moves at a constant velocity of 4 ft/s when a shearing force is applied. The separation distance between the plates is a uniform 0.05 in. Assume the velocity distribution in the fluid is linear. Determine the following: 4. the shear stress in the fluid (lbf/in2)...
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...
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