Navier Stokes equation of motion can be shown below in index notation.
Writing out the equation of motion in words equals the
following
Write out the equation of continuity in words?
mass x acceleration- body force + pressure gradient force + viscous force
Equations of Continuity: =0
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Navier Stokes equation of motion can be shown below in index notation. Writing out the equation of motion in words equals the following Write out the equation of continuity in words? Equations of Mo...
a) Write the governing equations (continuity and Navier Stokes) for a 1-D steady viscous flow in...
a) Write the governing equations (continuity and Navier Stokes) for a 1-D steady viscous flow in a rigid pipe. b) A patient who has normal blood pressure (systolic and diastolic also has hardening of the arteries, including the brachial artery in the upper arm. Will this patient's measured blood pressure be larger than the actual value, and why or why not?
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...
Tutorial 2. Incompressible Navier-Stokes equations 18 September, 4-5 pm in FN2 In Lecture Notes 1 the Navier-Stokes equ...
Tutorial 2. Incompressible Navier-Stokes equations 18 September, 4-5 pm in FN2 In Lecture Notes 1 the Navier-Stokes equations (momentum balance) for incompressible flow were derived. They were eventually written in the following form dr In this equation, the viscosity μ and the density ρ are constants. We now consider two simple flow configurations. Config. 1. The steady state flow of a liquid in the space between two very large static parallel plates at distance H of each other in the...
An incompressible viscous fluid is placed between horizontal, infinite parallel plates as shown. The two plates...
An incompressible viscous fluid is placed between horizontal, infinite parallel plates as shown. The two plates move in the same direction but with different velocities, U1 and U2. The pressure gradient in the x direction is zero and the only body force is due to the fluid weight. Using the continuity and the Navier-Stokes equations, find an expression for the velocity profile between the plates. Show ALL work for full credit. U1 V=O b KO wo U2
An incompressible viscous fluid is placed between horizontal, infinite parallel plates as shown. The two plates...
An incompressible viscous fluid is placed between horizontal, infinite parallel plates as shown. The two plates move in the same direction but with different velocities, U1 and U2. The pressure gradient in the x direction is zero and the only body force is due to the fluid weight. Using the continuity and the Navier-Stokes equations, find an expression for the velocity profile between the plates. Show ALL work for full credit. U1 V=O g u K wo U2
A. In the table below, identify which of the circled terms of the governing equations can...
A. In the table below, identify which of the circled terms of
the governing equations can be neglected
by the given assumption. Write the number of the term in the table.
Some assumptions relate
to multiple terms, include them all.
B. Write the mathematical equations describing the
appropriate boundary conditions and identify
them in words.
C. Applying the appropriate boundary conditions,
solve the differential equation remaining after
appropriate terms have been neglected to determine the velocity
profile in the film: d^2(w)/dx^2 =...
3. For experiment A, use equations 1&3 to develop a general equation for the value of...
3. For experiment A, use equations 1&3 to develop a general equation for the value of tension (T) based on the values of the two masses. You will need this later to answer lab question (4), so write it in now. 4. Based on the "net force" and "total mass" approach that was used to derive equations 3,4, and 5; develop the equation for acceleration of two masses (m, and m2) hanging vertically from either side of a frictionless pulley....
just 18.3 In other words, the center of mass moves as a free particle (no external...
just 18.3
In other words, the center of mass moves as a free particle (no external force) of mass m. The solution for R corre- sponds to uniform straight-line motion, and eliminates three of the six independent variables in the original equations of motion (three components each of, and r. Let us take, as the remaining three independent variables, the three components of r -. To ma- nipulate the original dynamical equations into a single vector equation for r. divide...
The construction of a water pistol is shown in the figure below. The cylinder with cross-sectional...
The construction of a water pistol is shown in the figure below. The cylinder with cross-sectional area A, is filled with water and when the piston is pushed (by pulling the trigger), water is forced out the tube with cross-sectional area A. The radius of the cylinder and tube are, respectively, 1.40 cm and 1.50 mm, and the center of the tube is a height h = 3.00 cm above the center of the cylinder. (Assume atmospheric pressure is 1.013...
Question 6.3 6.3 Consider a double mass-spring system with two masses of M and m on...
Question 6.3
6.3 Consider a double mass-spring system with two masses of M and m on a frictionless surface, as shown in Figure 6.30. Mass m is connected to M by a spring of constant k and rest length lo. Mass M is connected to a fixed wall by a spring of constant k and rest length lo and a damper with constant b. Find the equations of motion of each mass. (HINT: See Tutorial 2.1.) risto M wa ww...
a) Write the governing equations (continuity and Navier Stokes) for a 1-D steady viscous flow in a rigid pipe. b) A patient who has normal blood pressure (systolic and diastolic also has hardening of the arteries, including the brachial artery in the upper arm. Will this patient's measured blood pressure be larger than the actual value, and why or why not?
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...
Tutorial 2. Incompressible Navier-Stokes equations 18 September, 4-5 pm in FN2 In Lecture Notes 1 the Navier-Stokes equations (momentum balance) for incompressible flow were derived. They were eventually written in the following form dr In this equation, the viscosity μ and the density ρ are constants. We now consider two simple flow configurations. Config. 1. The steady state flow of a liquid in the space between two very large static parallel plates at distance H of each other in the...
An incompressible viscous fluid is placed between horizontal, infinite parallel plates as shown. The two plates move in the same direction but with different velocities, U1 and U2. The pressure gradient in the x direction is zero and the only body force is due to the fluid weight. Using the continuity and the Navier-Stokes equations, find an expression for the velocity profile between the plates. Show ALL work for full credit. U1 V=O b KO wo U2
An incompressible viscous fluid is placed between horizontal, infinite parallel plates as shown. The two plates move in the same direction but with different velocities, U1 and U2. The pressure gradient in the x direction is zero and the only body force is due to the fluid weight. Using the continuity and the Navier-Stokes equations, find an expression for the velocity profile between the plates. Show ALL work for full credit. U1 V=O g u K wo U2
A. In the table below, identify which of the circled terms of
the governing equations can be neglected
by the given assumption. Write the number of the term in the table.
Some assumptions relate
to multiple terms, include them all.
B. Write the mathematical equations describing the
appropriate boundary conditions and identify
them in words.
C. Applying the appropriate boundary conditions,
solve the differential equation remaining after
appropriate terms have been neglected to determine the velocity
profile in the film: d^2(w)/dx^2 =...
3. For experiment A, use equations 1&3 to develop a general equation for the value of tension (T) based on the values of the two masses. You will need this later to answer lab question (4), so write it in now. 4. Based on the "net force" and "total mass" approach that was used to derive equations 3,4, and 5; develop the equation for acceleration of two masses (m, and m2) hanging vertically from either side of a frictionless pulley....
just 18.3
In other words, the center of mass moves as a free particle (no external force) of mass m. The solution for R corre- sponds to uniform straight-line motion, and eliminates three of the six independent variables in the original equations of motion (three components each of, and r. Let us take, as the remaining three independent variables, the three components of r -. To ma- nipulate the original dynamical equations into a single vector equation for r. divide...
The construction of a water pistol is shown in the figure below. The cylinder with cross-sectional area A, is filled with water and when the piston is pushed (by pulling the trigger), water is forced out the tube with cross-sectional area A. The radius of the cylinder and tube are, respectively, 1.40 cm and 1.50 mm, and the center of the tube is a height h = 3.00 cm above the center of the cylinder. (Assume atmospheric pressure is 1.013...
Question 6.3
6.3 Consider a double mass-spring system with two masses of M and m on a frictionless surface, as shown in Figure 6.30. Mass m is connected to M by a spring of constant k and rest length lo. Mass M is connected to a fixed wall by a spring of constant k and rest length lo and a damper with constant b. Find the equations of motion of each mass. (HINT: See Tutorial 2.1.) risto M wa ww...
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