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4. An incompressible fluid with viscosity u and density p was contained in pipe of length...
2. Consider a polymer (with density p and viscosity u) flowing in between two parallel plates...
2. Consider a polymer (with density p and viscosity u) flowing in between two parallel plates in a vertical position. Both plates are stationary at x = 0 and x = h. A downward pressure is applied - dp/dz which is constant across the z-direction, which is also aided by gravity acting on the negative z-direction. Starting with the Navier-Stokes equations, find the simplified equation that defines the fluid velocity vz. State your assumptions to achieve this simplified equation. (7pts)...
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...
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...
Starting from the expression for the flow rate in a pipe, Q. for incompressible fluid: Q=T...
Starting from the expression for the flow rate in a pipe, Q. for incompressible fluid: Q=T R* Ap /(8 uL) (1) where R is the pipe radius, Ap is the pressure difference between the inlet and the outlet sections. u is the fluid density, and L is the pipe length. please prove that: 4t/(0.5 p v)= 64 /Re (2) where tw is the wall shear stress, and p is the liquid density and v is the average velocity in the...
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...
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...
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...
2) (LON3) (30 points) Given that; Force =f(flow velocity, body length, fluid density, fluid viscosity, speed...
2) (LON3) (30 points) Given that; Force =f(flow velocity, body length, fluid density, fluid viscosity, speed of sound) What is the minimum number of required experiments to express the force in terms of gven independent parameters. Find the dimensionless parameters in order to correlate the experimental data. (Assume that at least 10 points are required to fit a meaningful curve through experimental points of one independent parameter)
A semi-infinite body of liquid, with constant density and viscosity, is bounded below by a horizontal...
A semi-infinite body of liquid, with constant density and viscosity, is bounded below by a horizontal surface. Initially, the fluid and solid are at rest. Then at time t = 0, the solid surface is set in motion in the positive x direction with a constant velocity vo = 10 m/s, as shown in Figure 4-1. y y = 5 cm t< 0 y = 0 cm Fluid at rest у y = 5 cm t = 0 y =...
vector calculus (2) The Navier-Stokes equation is the fundamental equation of fluid dynamics that models the...
vector calculus
(2) The Navier-Stokes equation is the fundamental equation of fluid dynamics that models the motion of water in everything from bathtubs to oceans. In one of its many forms (incompressible, viscous flow), the equation is Ae +(V.V)V)-Vp+ p(V.V at In this notation V = (u, v, w) is the three-dimensional velocity field, p is the (scalar) pressure, p is the constant density of the fluid, and is the constant viscosity. Write out the three component equations of this...
2. Consider a polymer (with density p and viscosity u) flowing in between two parallel plates in a vertical position. Both plates are stationary at x = 0 and x = h. A downward pressure is applied - dp/dz which is constant across the z-direction, which is also aided by gravity acting on the negative z-direction. Starting with the Navier-Stokes equations, find the simplified equation that defines the fluid velocity vz. State your assumptions to achieve this simplified equation. (7pts)...
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...
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...
Starting from the expression for the flow rate in a pipe, Q. for incompressible fluid: Q=T R* Ap /(8 uL) (1) where R is the pipe radius, Ap is the pressure difference between the inlet and the outlet sections. u is the fluid density, and L is the pipe length. please prove that: 4t/(0.5 p v)= 64 /Re (2) where tw is the wall shear stress, and p is the liquid density and v is the average velocity in the...
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...
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...
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...
2) (LON3) (30 points) Given that; Force =f(flow velocity, body length, fluid density, fluid viscosity, speed of sound) What is the minimum number of required experiments to express the force in terms of gven independent parameters. Find the dimensionless parameters in order to correlate the experimental data. (Assume that at least 10 points are required to fit a meaningful curve through experimental points of one independent parameter)
A semi-infinite body of liquid, with constant density and viscosity, is bounded below by a horizontal surface. Initially, the fluid and solid are at rest. Then at time t = 0, the solid surface is set in motion in the positive x direction with a constant velocity vo = 10 m/s, as shown in Figure 4-1. y y = 5 cm t< 0 y = 0 cm Fluid at rest у y = 5 cm t = 0 y =...
vector calculus
(2) The Navier-Stokes equation is the fundamental equation of fluid dynamics that models the motion of water in everything from bathtubs to oceans. In one of its many forms (incompressible, viscous flow), the equation is Ae +(V.V)V)-Vp+ p(V.V at In this notation V = (u, v, w) is the three-dimensional velocity field, p is the (scalar) pressure, p is the constant density of the fluid, and is the constant viscosity. Write out the three component equations of this...
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