Fluid Dynamics Help
Fluid dynamics conceptual problem help
Fluid fills the space between two parallel plates. The differential equation that describes the instantaneous fluid velocity for unsteady flow with the fluid moving parallel to the walls is (shown in picture).
The lower plate is stationary and the upper plate oscillates in the x-direction with a frequency ω and an amplitude in the plate velocity of U. Use the characteristic dimensions to normalize the differential equation and obtain the dimensionless groups that characterize the flow.
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1. As seenfrom figure, there is a laminar and viscous fluid flow betweentwo parallel plates where...
1. As seenfrom figure, there is a laminar and viscous fluid flow betweentwo parallel plates where the one is moving with velocity y, other one is stationary. There exists pressure gradient in x direction. The bottom stationary plate is a porous plate andfluid is injected into the channel with V velocity. If theflow is steady, fully developed and incompressible flow, derive the velocity profile. Uo Vo
1. As seenfrom figure, there is a laminar and viscous fluid flow betweentwo parallel...
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...
Question 5 [20 marks) Consider Coutte flow, which occurs when we have a fluid suspended between two parallel plates, on...
Question 5 [20 marks) Consider Coutte flow, which occurs when we have a fluid suspended between two parallel plates, one of which is moving and the other of which is stationary. The velocity profile between these two plates is linear. We have water between these two plates and distance separating them of 1 mm. Given this information: (a) What is the force exerted on the stationary plate per m2 if the moving plate has a velocity of 0.1 m/s in...
An incompressible fluid flows between two porous, parallel flat plates as shown in the Figure below....
An incompressible fluid flows between two porous, parallel flat plates as shown in the Figure below. An identical fluid is injected at a constant speed V through the bottom plate and simultaneously extracted from the upper plate at the same velocity. There is no gravity force in x and y directions (g-g,-0). Assume the flow to be steady, fully-developed, 2D, and the pressure gradient in the x direction to be a constant P = constant). (a) Write the continuity equation...
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 a Couette flow between two flat plates: One plate is stationary, while the other plate...
Consider a Couette flow between two flat plates: One plate is stationary, while the other plate is moving with a velocity vo; the distance between the plates is h. Realize that the density and the viscosity of the fluid are roughly constant. You may also presume that the velocity is mostly unidirectional, solely varying in its perpendicular direction. In turn, formulate and solve the differential equation which governs the velocity profile!
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...
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...
The Navier-Stokes equations are a system of non-linear, partial-differential equations that describe fluid flows. In the...
The Navier-Stokes equations are a system of non-linear, partial-differential equations that describe fluid flows. In the incompressible limit, the density of the fluid may be regarded as a constant, and the system of equations becomes, Because of the non-linearities, there are very few exact solutions that are known for these equations. One of the exact solutions is pressure-driven channel (or pipe) flow, also known as Poiseuille flow. In this flow, all solid, no-slip walls are parallel to the x-axis, and...
283 Laminar fow in a narrow slit (see Fig, 2B.3), Fluid in Fluid outFig. 2B.3 Flow...
283 Laminar fow in a narrow slit (see Fig, 2B.3), Fluid in Fluid outFig. 2B.3 Flow through a slit, with B< W<<L a) A Newtonian fluid is in laminar flow in a narrow slit formed by two parallel walls a dis tance 2B apart. It is understood that B <W, so that "edge effects" are unimportant. Make a differential momentum balance, and obtain the following expressions for the momentum-flux and velocity distributions ", " (부). (2B.3-1) (P )B (2B.3-2) In...
1. As seenfrom figure, there is a laminar and viscous fluid flow betweentwo parallel plates where the one is moving with velocity y, other one is stationary. There exists pressure gradient in x direction. The bottom stationary plate is a porous plate andfluid is injected into the channel with V velocity. If theflow is steady, fully developed and incompressible flow, derive the velocity profile. Uo Vo
1. As seenfrom figure, there is a laminar and viscous fluid flow betweentwo parallel...
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...
Question 5 [20 marks) Consider Coutte flow, which occurs when we have a fluid suspended between two parallel plates, one of which is moving and the other of which is stationary. The velocity profile between these two plates is linear. We have water between these two plates and distance separating them of 1 mm. Given this information: (a) What is the force exerted on the stationary plate per m2 if the moving plate has a velocity of 0.1 m/s in...
An incompressible fluid flows between two porous, parallel flat plates as shown in the Figure below. An identical fluid is injected at a constant speed V through the bottom plate and simultaneously extracted from the upper plate at the same velocity. There is no gravity force in x and y directions (g-g,-0). Assume the flow to be steady, fully-developed, 2D, and the pressure gradient in the x direction to be a constant P = constant). (a) Write the continuity equation...
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 a Couette flow between two flat plates: One plate is stationary, while the other plate is moving with a velocity vo; the distance between the plates is h. Realize that the density and the viscosity of the fluid are roughly constant. You may also presume that the velocity is mostly unidirectional, solely varying in its perpendicular direction. In turn, formulate and solve the differential equation which governs the velocity profile!
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...
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...
The Navier-Stokes equations are a system of non-linear, partial-differential equations that describe fluid flows. In the incompressible limit, the density of the fluid may be regarded as a constant, and the system of equations becomes, Because of the non-linearities, there are very few exact solutions that are known for these equations. One of the exact solutions is pressure-driven channel (or pipe) flow, also known as Poiseuille flow. In this flow, all solid, no-slip walls are parallel to the x-axis, and...
283 Laminar fow in a narrow slit (see Fig, 2B.3), Fluid in Fluid outFig. 2B.3 Flow through a slit, with B< W<<L a) A Newtonian fluid is in laminar flow in a narrow slit formed by two parallel walls a dis tance 2B apart. It is understood that B <W, so that "edge effects" are unimportant. Make a differential momentum balance, and obtain the following expressions for the momentum-flux and velocity distributions ", " (부). (2B.3-1) (P )B (2B.3-2) In...
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