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Hypothetical velocity profile in a circular pipe is given by following equation V = V1 here...
10 points Hypothetical velocity profile in a circular pipe is given by following equation V -...
10 points Hypothetical velocity profile in a circular pipe is given by following equation V - V.(1 - here Vis maximum velocity and ro is the radius of pipe and varies from 0 tor. For this scenario, determine the mean velocity v 4V 2V
3. Water flowing through a pipe assumes a laminar-flow velocity profile at some section is parabolic:...
3. Water flowing through a pipe assumes a laminar-flow velocity profile at some section is parabolic: u(0) -4J Figure 2 where u(r) is the velocity at any position r, ß is a constant,-11s the viscosity of water, and r is the radial distance from the pipe centerline. (a) Develop an equation for u(r) assuming a parabolic velocity profile and using the known velocities at the walls u(ro)-0 and the center u(0) (Just use symbols). (b) Develop an equation for shear...
Q5. Sketching a suitable control volume, show that the velocity profile V(r) for steady, fully laminar...
Q5. Sketching a suitable control volume, show that the velocity profile V(r) for steady, fully laminar flow in a horizontal pipe is given by V(r)- whereis is the pressure drop per unit length of pipe, R is the pipe radius and u the dynamic viscosity of the fluid. (10 marks) Thereafter develop Poiseuille's law for the volume flow rate O in the form SuL (10 marks) Hence show that the head loss h is given by where Vis the mean...
2. (20 marks) The fully-developed, laminar fluid flow through a circular pipe is considered to be...
2. (20 marks) The fully-developed, laminar fluid flow through a circular pipe is considered to be one dimensional with a velocity profile given by u(r) = Umax(1 - 52/R2), where R is the radius of the pipe, r is the radial distance from the center of the pipe, and Umax is the maximum flow velocity at the center of the pipe. a) Derive a relation for the drag force applied by the fluid on a section of the pipe of...
Water flows in a pipe that has a 4 ft diameter and the following hypothetical velocity...
Water flows in a pipe that has a 4 ft diameter and the following hypothetical velocity distribution: The velocity is maximum at the centerline and decreases linearly with r to a minimum at the pipe wall. If Vmax = 17 ft/s and Vmin = 10 ft/s, what is the discharge in cubic feet per second and in gallons per minute? The volume flow rate is given by the integral of the velocity over the area Using the correct expression for...
Water flows in a pipe that has a 4 ft diameter and the following hypothetical velocity...
Water flows in a pipe that has a 4 ft diameter and the following hypothetical velocity distribution: The velocity is maximum at the centerline and decreases linearly with r to a minimum at the pipe wall. If Vmax = 15 ft/s and Vmin = 12 ft/s, what is the discharge in cubic feet per second and in gallons per minute? The volume flow rate is given by the integral of the velocity over the area Q = -fvaa Using the...
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)...
An incompressible Newtonian fluid flow through a horizontal circular tube is shown in the following figure....
An incompressible Newtonian fluid flow through a horizontal circular tube is shown in the following figure. We assume that the flow is steady, and its direction is parallel to the wall. By using the Navier-Stokes equations. determine the velocity profile and calculate the mean velocity and maximum velocity; Please give the details about how to simplify the N-S equation, how to integrate the simplified N-S equations with the proper boundary conditions, and the relationship between the mean velocity and maximum...
Problem 5. Consider a (i) steady, (ii) incompressible, axisymmetric, (iv) fully- developed, (v) constant viscosity, (vi) laminar flow in a circular pipe. Assume that the pipe is horizontal, so that a...
Problem 5. Consider a (i) steady, (ii) incompressible, axisymmetric, (iv) fully- developed, (v) constant viscosity, (vi) laminar flow in a circular pipe. Assume that the pipe is horizontal, so that any gravitational effects can be ignored It is known that an incompressible, constant viscosity fluid can be described by the continuity equation in cylindrical coordinates together with the Naiver-Stokes equations (ak.a., momentum eqns) in cylindrical coor- dinates Ov 00. Or 9-moment um 11ap 2-momentum plus the appropriate boundary conditions. Starting...
Only need help with Question 3, thanks ;) The actual velocity profile is given by the...
Only need help with Question 3, thanks ;)
The actual velocity profile is given by the Poiseuille equation as follows: ()APR where AP is the pressure driving force, R is the tube radius, u is the fluid viscosity, Lis the tube length, and r is the radial position of interest. A couple of notes: . Assume that the fluid has a viscosity similar to water (rester 103 Pa s) Winter 2019 Il. The radial position r is defined to be...
10 points Hypothetical velocity profile in a circular pipe is given by following equation V - V.(1 - here Vis maximum velocity and ro is the radius of pipe and varies from 0 tor. For this scenario, determine the mean velocity v 4V 2V
3. Water flowing through a pipe assumes a laminar-flow velocity profile at some section is parabolic: u(0) -4J Figure 2 where u(r) is the velocity at any position r, ß is a constant,-11s the viscosity of water, and r is the radial distance from the pipe centerline. (a) Develop an equation for u(r) assuming a parabolic velocity profile and using the known velocities at the walls u(ro)-0 and the center u(0) (Just use symbols). (b) Develop an equation for shear...
Q5. Sketching a suitable control volume, show that the velocity profile V(r) for steady, fully laminar flow in a horizontal pipe is given by V(r)- whereis is the pressure drop per unit length of pipe, R is the pipe radius and u the dynamic viscosity of the fluid. (10 marks) Thereafter develop Poiseuille's law for the volume flow rate O in the form SuL (10 marks) Hence show that the head loss h is given by where Vis the mean...
2. (20 marks) The fully-developed, laminar fluid flow through a circular pipe is considered to be one dimensional with a velocity profile given by u(r) = Umax(1 - 52/R2), where R is the radius of the pipe, r is the radial distance from the center of the pipe, and Umax is the maximum flow velocity at the center of the pipe. a) Derive a relation for the drag force applied by the fluid on a section of the pipe of...
Water flows in a pipe that has a 4 ft diameter and the following hypothetical velocity distribution: The velocity is maximum at the centerline and decreases linearly with r to a minimum at the pipe wall. If Vmax = 17 ft/s and Vmin = 10 ft/s, what is the discharge in cubic feet per second and in gallons per minute? The volume flow rate is given by the integral of the velocity over the area Using the correct expression for...
Water flows in a pipe that has a 4 ft diameter and the following hypothetical velocity distribution: The velocity is maximum at the centerline and decreases linearly with r to a minimum at the pipe wall. If Vmax = 15 ft/s and Vmin = 12 ft/s, what is the discharge in cubic feet per second and in gallons per minute? The volume flow rate is given by the integral of the velocity over the area Q = -fvaa Using the...
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)...
An incompressible Newtonian fluid flow through a horizontal circular tube is shown in the following figure. We assume that the flow is steady, and its direction is parallel to the wall. By using the Navier-Stokes equations. determine the velocity profile and calculate the mean velocity and maximum velocity; Please give the details about how to simplify the N-S equation, how to integrate the simplified N-S equations with the proper boundary conditions, and the relationship between the mean velocity and maximum...
Problem 5. Consider a (i) steady, (ii) incompressible, axisymmetric, (iv) fully- developed, (v) constant viscosity, (vi) laminar flow in a circular pipe. Assume that the pipe is horizontal, so that any gravitational effects can be ignored It is known that an incompressible, constant viscosity fluid can be described by the continuity equation in cylindrical coordinates together with the Naiver-Stokes equations (ak.a., momentum eqns) in cylindrical coor- dinates Ov 00. Or 9-moment um 11ap 2-momentum plus the appropriate boundary conditions. Starting...
Only need help with Question 3, thanks ;)
The actual velocity profile is given by the Poiseuille equation as follows: ()APR where AP is the pressure driving force, R is the tube radius, u is the fluid viscosity, Lis the tube length, and r is the radial position of interest. A couple of notes: . Assume that the fluid has a viscosity similar to water (rester 103 Pa s) Winter 2019 Il. The radial position r is defined to be...
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