The average velocity < v > of a viscous fluid through a pipe is proportional to...
The average velocity < v > of a viscous fluid through a pipe is proportional to the drop in pressure ∆P, length L, radius of the pipe r, and viscosity of the fluid η (units: kg/m/s). Performing various experiments it has been determined that the velocity is directly proportional to the drop in pressure divided by the length. Determine the dependence of < v > on these quantities.
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The average velocity < v > of a viscous fluid through a
pipe is proportional to...
When an object moves through a fluid, the fluid exerts a viscous force F on the...
When an object moves through a fluid, the fluid exerts a viscous force F on the object that tends to slow it down. For a small sphere of radius R, moving slowly with a speed v, the magnitude of the viscous force is given by Stokes, law, F = 6πηRv, where η is the viscosity of the fluid. (a) What is the viscous force on a sphere of radius R = 8.9 x 10-4 m falling through water (η =...
What does Δp = QR mean in words? Pushing a viscous fluid through a pipe requires...
What does Δp = QR mean in words? Pushing a viscous fluid through a pipe requires a drop in pressure along the direction in which the fluid is flowing through the pipe. If there is no pressure difference across a pipe, the flow is 1/R. If you increase the flow of a viscous fluid, you increase the pressure at the end of the pipe toward which the fluid if flowing. A viscous fluid will always move more and more quickly...
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...
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)...
1) 25pt)Poiseuille’s Law is a fundamental law of fluid dynamics that describes the flow velocity of...
1) 25pt)Poiseuille’s Law is a fundamental law of fluid dynamics that describes the flow velocity of a viscous incompressible fluid in a cylinder. It says that in a cylinder of radius R and length L, the velocity of the fluid r (where r ≤ R) units from the center line of the cylinder is: ? = ? 4?? (? 2 − ? 2 ), where P is the difference in the pressure between the ends of the cylinder and ν...
Ignore question [1], just need the problem description from it. [1] Water flowing in a pipe...
Ignore question [1], just need
the problem description from it.
[1] Water flowing in a pipe is determined to be moving at the velocities given in the diagram below. The higher level is 3 meters above the lower one and the pressure in the lower portion is measured to be 200 kPa. Determine the pressure inside the upper pipe Treat the water as an ideal fluid obeying Bernoulli's equation. Consider the path connecting poin in the lower pipe with point...
12. A fluid is flowing through a pipe with a radius of 5.1 x 10-3 m....
12. A fluid is flowing through a pipe with a radius of 5.1 x 10-3 m. The viscosity of the fluid is 1.0 x 10-3 Pa-s. A flow rate of 2.8 x 10-4 m3/s is required, and it is found that a pressure difference of 1.8 × 103 Pa is needed to drive this flow. With this information, calculate the length of the pipe. Hint: assume the flow is viscous flow (a) 1.7 m (b) 5.9 m (c) 3.2 cm...
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...
Page 4 of 8 (30 points) The velocity of the of Poiseuile Bow a within a...
Page 4 of 8 (30 points) The velocity of the of Poiseuile Bow a within a pipe can be determined using the relationahip 4. ApR where u is the viscosity of the fluid, R is the radius of the pipe, Ap is the measured pressure drop L is the length of the test section The following data were gathered or estimated during the measuring process: R 5.50+0.02 in -6.75+0.02lbfs/in The length of the test section L was measured 6 times...
please solve (va20) for me thanks!! :) V VISCOUS FLOWS Page 38 nar flow between two infinite plates a distance h apart driven by a pressure gra- Va20. For lami dient, the velocity profile is [constan...
please solve (va20) for me thanks!! :)
V VISCOUS FLOWS Page 38 nar flow between two infinite plates a distance h apart driven by a pressure gra- Va20. For lami dient, the velocity profile is [constant] [linear] [parabolic] [hyperbolic] [elliptic] [error func- tion], and the flow rate Q is proportional to h to the power is driven by the top plate moving at a speed U in the absence of any pressure gradient, the velocity profile is [constant] linearl Iparabolic]...
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...
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)...
Ignore question [1], just need
the problem description from it.
[1] Water flowing in a pipe is determined to be moving at the velocities given in the diagram below. The higher level is 3 meters above the lower one and the pressure in the lower portion is measured to be 200 kPa. Determine the pressure inside the upper pipe Treat the water as an ideal fluid obeying Bernoulli's equation. Consider the path connecting poin in the lower pipe with point...
12. A fluid is flowing through a pipe with a radius of 5.1 x 10-3 m. The viscosity of the fluid is 1.0 x 10-3 Pa-s. A flow rate of 2.8 x 10-4 m3/s is required, and it is found that a pressure difference of 1.8 × 103 Pa is needed to drive this flow. With this information, calculate the length of the pipe. Hint: assume the flow is viscous flow (a) 1.7 m (b) 5.9 m (c) 3.2 cm...
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...
Page 4 of 8 (30 points) The velocity of the of Poiseuile Bow a within a pipe can be determined using the relationahip 4. ApR where u is the viscosity of the fluid, R is the radius of the pipe, Ap is the measured pressure drop L is the length of the test section The following data were gathered or estimated during the measuring process: R 5.50+0.02 in -6.75+0.02lbfs/in The length of the test section L was measured 6 times...
please solve (va20) for me thanks!! :)
V VISCOUS FLOWS Page 38 nar flow between two infinite plates a distance h apart driven by a pressure gra- Va20. For lami dient, the velocity profile is [constant] [linear] [parabolic] [hyperbolic] [elliptic] [error func- tion], and the flow rate Q is proportional to h to the power is driven by the top plate moving at a speed U in the absence of any pressure gradient, the velocity profile is [constant] linearl Iparabolic]...
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