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283 Laminar fow in a narrow slit (see Fig, 2B.3), Fluid in Fluid outFig. 2B.3 Flow...
3 PL 23.5 Laminar slit flow with a moving wall ("plane Couette flow"). Extend Problem 23.4...
3 PL 23.5 Laminar slit flow with a moving wall ("plane Couette flow"). Extend Problem 23.4 by allow- ing the wall at x B to move in the positive z direction at a steady speed 0 Obtain (a) the shear-stress distribution, and (b) the velocity distribution. 12 Lipuli on Draw carefully labeled sketches of these functions. Answers: (a) „(v) = (*7*2)=- (b) v.Cx) = (*72)P" [1-(0))+ (1+ }) - )B2 ( (b) v(x) = — 1 ... thin it may...
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...
Consider a fully developed laminar flow of an incompressible Newtonian fluid between two infinite parallel plates,...
Consider a fully developed laminar flow of an incompressible
Newtonian fluid between two infinite parallel plates, separated by
a distance of 2B. The z coordinate is the direction of the flow.
The width of the plates is 2W (direction y). The coordinate axis is
located half of the 2 plates.
a) Obtain the distribution of speeds in steady state.
b) Obtain the expression for the maximum velocity and write the
velocity distribution of part a) as a function of the...
fluid mechanics A steady, incompressible, and laminar flow of a fluid of viscosity u flows through...
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...
Tangential laminar flow of a Newtonian fluid with constant density and occurring between two vertical coaxial...
Tangential laminar flow of a Newtonian fluid with constant density and occurring between two vertical coaxial cylinders in which the outer rotating with an angular velocity of ω and the inner cylinder is fixed a. Write the simplified continuity equation and the simplified momentum balance equations using necessary assumptions and determine the velocity. b. Determine the shear stress distributions for this flow. c. Calculate the necessary torque. outside cylinder rotates 2 inside cylinder Figure: Top view of the coaxial cylinders
Fluid is Non-Newtonian. (3) Consider the steady laminar flow between the coaxial cylinders shown below. The...
Fluid is Non-Newtonian.
(3) Consider the steady laminar flow between the coaxial cylinders shown below. The inner cylinder rotates with angular velocity 2 and the outer cylinder is stationary. The no-slip condition applies at the inner and outer cylinder surfaces and we are considering the cylinders to be very long in the 2-direction hence we may ignore edge effects near the top and bottom surfaces. - R2 Assume that gravity is negligible, v, is zero and that are zero for...
A fluid flow over a solid surface with a laminar boundary layer velocity profile is approximated...
A fluid flow over a solid surface with a laminar boundary layer velocity profile is approximated by the following equation: Ý = 2 () – ()* for y so and, 4 = 0 for y> 8 i). Show that this velocity profile satisfies the appropriate boundary conditions. ii) Determine the boundary layer thickness, 8 = 8(x) by using the momentum integral equation for the equation in Question 3(b)(i).
3. (30 points) Consider a two-dimensional flow of a Newtonian fluid in which the velocity field...
3. (30 points) Consider a two-dimensional flow of a Newtonian fluid in which the velocity field is given by 2ry (a) (5 points) Is this flow incompressible? b) (10 points) Use the x-momentum equation to determine ap/aa (e) (10 points) Use the y-momentum equation to determine ap/dy (d) (5 points) Use the above results to integrate and solve for p(x, y). Evaluate constant of integration by setting p(0,0- Pa as a condition (e) (45 Bonus points) Determine the viscouas stress...
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...
3.0, Radial Flow between Concentric Spheres Consider an isothermal, incompressible fluid flowing radially between t...
3.0, Radial Flow between Concentric Spheres Consider an isothermal, incompressible fluid flowing radially between two concentric porous spherical shells. (See Fig. 3.0.) Assume stecady laminar flow withu- ul) Direction of flow flow between concentric porous spheres. Fig. 10. Radial Note that here the velocity is not assumed zero at the solid surfaces. Show by use of the cquation of continuity that a. (3.0- where y is a constant. b. Show by use of the equations of motion that the pressure...
3 PL 23.5 Laminar slit flow with a moving wall ("plane Couette flow"). Extend Problem 23.4 by allow- ing the wall at x B to move in the positive z direction at a steady speed 0 Obtain (a) the shear-stress distribution, and (b) the velocity distribution. 12 Lipuli on Draw carefully labeled sketches of these functions. Answers: (a) „(v) = (*7*2)=- (b) v.Cx) = (*72)P" [1-(0))+ (1+ }) - )B2 ( (b) v(x) = — 1 ... thin it may...
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...
Consider a fully developed laminar flow of an incompressible
Newtonian fluid between two infinite parallel plates, separated by
a distance of 2B. The z coordinate is the direction of the flow.
The width of the plates is 2W (direction y). The coordinate axis is
located half of the 2 plates.
a) Obtain the distribution of speeds in steady state.
b) Obtain the expression for the maximum velocity and write the
velocity distribution of part a) as a function of the...
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...
Tangential laminar flow of a Newtonian fluid with constant density and occurring between two vertical coaxial cylinders in which the outer rotating with an angular velocity of ω and the inner cylinder is fixed a. Write the simplified continuity equation and the simplified momentum balance equations using necessary assumptions and determine the velocity. b. Determine the shear stress distributions for this flow. c. Calculate the necessary torque. outside cylinder rotates 2 inside cylinder Figure: Top view of the coaxial cylinders
Fluid is Non-Newtonian.
(3) Consider the steady laminar flow between the coaxial cylinders shown below. The inner cylinder rotates with angular velocity 2 and the outer cylinder is stationary. The no-slip condition applies at the inner and outer cylinder surfaces and we are considering the cylinders to be very long in the 2-direction hence we may ignore edge effects near the top and bottom surfaces. - R2 Assume that gravity is negligible, v, is zero and that are zero for...
A fluid flow over a solid surface with a laminar boundary layer velocity profile is approximated by the following equation: Ý = 2 () – ()* for y so and, 4 = 0 for y> 8 i). Show that this velocity profile satisfies the appropriate boundary conditions. ii) Determine the boundary layer thickness, 8 = 8(x) by using the momentum integral equation for the equation in Question 3(b)(i).
3. (30 points) Consider a two-dimensional flow of a Newtonian fluid in which the velocity field is given by 2ry (a) (5 points) Is this flow incompressible? b) (10 points) Use the x-momentum equation to determine ap/aa (e) (10 points) Use the y-momentum equation to determine ap/dy (d) (5 points) Use the above results to integrate and solve for p(x, y). Evaluate constant of integration by setting p(0,0- Pa as a condition (e) (45 Bonus points) Determine the viscouas stress...
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...
3.0, Radial Flow between Concentric Spheres Consider an isothermal, incompressible fluid flowing radially between two concentric porous spherical shells. (See Fig. 3.0.) Assume stecady laminar flow withu- ul) Direction of flow flow between concentric porous spheres. Fig. 10. Radial Note that here the velocity is not assumed zero at the solid surfaces. Show by use of the cquation of continuity that a. (3.0- where y is a constant. b. Show by use of the equations of motion that the pressure...
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