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2. In the figure below a cylindrical pipe with radius R and length L is shown....
The laminar flow of a permanent incompressible Newtonian fluid in a long cylindrical pipe with a...
The laminar flow of a permanent incompressible Newtonian fluid in a long cylindrical pipe with a diameter D in vertical position is considered. Gravitational effects are taken into account, flow is carried out with a constant pressure gradient and gravity effect in the z- direction. a. Express the problem on the figure, write the given and accepted. b. Find the velocity profile in the fluid. c. Develop the relations that express the volumetric flow and shear stress in the pipe...
4. An incompressible fluid with viscosity u and density p was contained in pipe of length...
4. An incompressible fluid with viscosity u and density p was contained in pipe of length L and radius R. Initially the fluid is in rest. At t=0, a pressure difference of AP is applied across the pipe length which induces the fluid flow in axial direction (V2) Only varies with time (t) and pipe radius (r). There is no effect of gravity. To describe the fluid flow characteristics, after the pressure gradient is applied, answer the following questions: a)...
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)
Step by step solution please A 16-inch gasoline pipe line is transport gasoline at a flow...
Step by step solution please
A 16-inch gasoline pipe line is transport gasoline at a flow rate of 200 gallon per minute. Please calculate how much pressure gradient dp/dx is needed, using the N-S equation provided in below? (Hint: Assuming the flow in the pipe line is laminar so you can use the Poisson flow to solve the problem. Dynamic viscosity of gasoline is 0.0006 N/m*2 second; density of gasoline is 0.77 kg/L.) Cylindrical coordinates (r.0,2) We consider an incompressible,...
L 2. Steady statemass balance: Water is flowing at steady state in a 0.1 meter-diameter pipe...
L 2. Steady statemass balance: Water is flowing at steady state in a 0.1 meter-diameter pipe with a maximum velocity (turbulent profile) of 0.3 meters/sec. The pipe then goes through an expansion, to where it is then flowing in a 0.5 meter-diameter pipe, and the flow regime has changed from turbulent to laminar. In the second section of pipe, calculate the velocity as (a) block flow profile (Vavg), and (b) maximum velocity in laminar flow profile? HINT: you will need...
A long, cylindrical non-conductor of radius R and length L is placed with it long axis...
A long, cylindrical non-conductor of radius R and length L is placed with it long axis along the Z-axis as shown The cylinder has a total charge Q distributed non-uniformly thrpughout its volume. The charge density is only a function of the radial distance "r" from the cylinder axis and varies as ρ(r):- where α is a constant Vr. 2 +9R2 c) What coordinate system will you use? L (xy,z), (p,o,Z), (,o,)) d) What variables will the magnitude of the...
A cylindrical conductor of area A and length L has a conductivity (σ-1/R) that varies as...
A cylindrical conductor of area A and length L has a conductivity (σ-1/R) that varies as ơ -now Find an algebraic relationship between the current density (VA), ơo, L and A if the conductor is connected to V volts DC
A cylindrical cork of radius R and length L is floating in a liquid such that...
A cylindrical cork of radius R and length L is floating in a liquid such that its axis of symmetry is vertical and half of the length of the cork is below the fluid (the density of the fluid is p), as in Figure 2. For this problem, ignore any effects from friction, drag and the viscosity of the fluid (a) Show that the density of the cork, Pe is half that of the fluid (Pe ps) (b) If the...
4) Figure 5 illustrates a solid cylindrical conductor having length L and uniform X-sectional area A....
4) Figure 5 illustrates a solid cylindrical conductor having length L and uniform X-sectional area A. The resistivity p of the cylinder is non-uniform and described by the function P(x) = Cx where is a constant and x is position measured along the length of the cylinder such that x = 0 at the left end and x = L at the right end. The terminals of an ideal Figures battery having emfE are connected to the opposing ends of...
2c. A insulating cylindrical shell with length L and inner radius a, outer radius b, has...
2c. A insulating cylindrical shell with length L and inner radius a, outer radius b, has uniform charge density p. Find the E, not near the ends, for three regions, ra, arb, r>b. * Note, a linear density A could also be given cross section 3c. An insulating shell has inner radius a and outer radius b and a uniform charge density p. Find E at all r (ra; arb; r> b)
4. An incompressible fluid with viscosity u and density p was contained in pipe of length L and radius R. Initially the fluid is in rest. At t=0, a pressure difference of AP is applied across the pipe length which induces the fluid flow in axial direction (V2) Only varies with time (t) and pipe radius (r). There is no effect of gravity. To describe the fluid flow characteristics, after the pressure gradient is applied, answer the following questions: a)...
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)
Step by step solution please
A 16-inch gasoline pipe line is transport gasoline at a flow rate of 200 gallon per minute. Please calculate how much pressure gradient dp/dx is needed, using the N-S equation provided in below? (Hint: Assuming the flow in the pipe line is laminar so you can use the Poisson flow to solve the problem. Dynamic viscosity of gasoline is 0.0006 N/m*2 second; density of gasoline is 0.77 kg/L.) Cylindrical coordinates (r.0,2) We consider an incompressible,...
L 2. Steady statemass balance: Water is flowing at steady state in a 0.1 meter-diameter pipe with a maximum velocity (turbulent profile) of 0.3 meters/sec. The pipe then goes through an expansion, to where it is then flowing in a 0.5 meter-diameter pipe, and the flow regime has changed from turbulent to laminar. In the second section of pipe, calculate the velocity as (a) block flow profile (Vavg), and (b) maximum velocity in laminar flow profile? HINT: you will need...
A long, cylindrical non-conductor of radius R and length L is placed with it long axis along the Z-axis as shown The cylinder has a total charge Q distributed non-uniformly thrpughout its volume. The charge density is only a function of the radial distance "r" from the cylinder axis and varies as ρ(r):- where α is a constant Vr. 2 +9R2 c) What coordinate system will you use? L (xy,z), (p,o,Z), (,o,)) d) What variables will the magnitude of the...
A cylindrical conductor of area A and length L has a conductivity (σ-1/R) that varies as ơ -now Find an algebraic relationship between the current density (VA), ơo, L and A if the conductor is connected to V volts DC
A cylindrical cork of radius R and length L is floating in a liquid such that its axis of symmetry is vertical and half of the length of the cork is below the fluid (the density of the fluid is p), as in Figure 2. For this problem, ignore any effects from friction, drag and the viscosity of the fluid (a) Show that the density of the cork, Pe is half that of the fluid (Pe ps) (b) If the...
4) Figure 5 illustrates a solid cylindrical conductor having length L and uniform X-sectional area A. The resistivity p of the cylinder is non-uniform and described by the function P(x) = Cx where is a constant and x is position measured along the length of the cylinder such that x = 0 at the left end and x = L at the right end. The terminals of an ideal Figures battery having emfE are connected to the opposing ends of...
2c. A insulating cylindrical shell with length L and inner radius a, outer radius b, has uniform charge density p. Find the E, not near the ends, for three regions, ra, arb, r>b. * Note, a linear density A could also be given cross section 3c. An insulating shell has inner radius a and outer radius b and a uniform charge density p. Find E at all r (ra; arb; r> b)
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