Problem 1: (mark 20% ) Obtain an expression for the shear stress of a Newtonian fluid...
Problem 4. In class we introduced the concept of a Newtonian fluid. A Newtonian Fluid is one in which the stress and strain rate relationship is linear and related by the fluid viscosity. Answer the following equations about Newtonian and Non-Newtonian fluid models. a) With a Newtonian Model, indicate what the shear forces are on the x-face of a fluid element. b) With a Newtonian Incompressible Model, indicate what the normal force is on the x-face of a fluid element—show...
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...
1. Some non-Newtonian fluids behave as a Bingham plastic for which shear stress can be expressed as + For laminar flow of a Bingham plastic in a horizontal pipe of radius R, the velocity profile is given as 4wr -R)+ (r-R), where AP/L is the constant pressure drop along the pipe per unit length, is the dynamic viscosity,r is the radial distance from the centerline, and is the yield stress of Bingham plastic. Develop a relation for (a) the shear...
, (20 pts) The Newtonian fluid is confined between an upper plate and a bottom f If its velocity profile is defined by u s(9y-0.1y3) rn m/s , where y is in mm, (a) determine the shear stress that the fluid exerts on the upper plate and bottom fixed surface and (b) indicate the direction of each shear stress. Take the fluid viscosity A0.482 N s/m2.
Problem 3. A 2D velocity field for an incompressible Newtonian fluid is given by u 12xy-62.3, u = 18x2y-4y3, where the velocity has unit m/s and x and y are in meters. (a) Determine the normal stresses ơzz and ơuy, and shear stress Try at the point x-1 m, y 1 m, where the pressure at this point is 6 kPa and dynamic viscosity is 1 Pa.s. (b) Sketch the magnitude and direction of the stress components.
Problem 3- For flow of an incompressible, Newtonian fluids between parallel plates, the velocity distribution between the plate is given by 1 dP 2μ dr where y is the direction from one plate (y-0) to another (y-w),and x is the direction of flow a) What is the expression for the rate of deformation matrix? b) What is the expression for the stress matrix? c) At the center of the flow y w/2, what is the direction of internal forcing due...
Consider a fully developed laminar flow of an incompressible
Newtonian fluid between two infinite parallel plates, separated by
a distance of 2B. The z coordinate is the direction of the flow.
The width of the plates is 2W (direction y). The coordinate axis is
located half of the 2 plates.
a) Obtain the distribution of speeds in steady state.
b) Obtain the expression for the maximum velocity and write the
velocity distribution of part a) as a function of the...
What is shear stress proportional to when applied to a fluid? Write the expression for shear stress. What is cavitation? Give an example of when this can occur. HTML Editor Explain water hammer. Provide an example. What is the difference between laminar and turbulent flow? What nondimensional parameter is used to determine if the flow is laminar or turbulent? (Hint: Ratio of inertial forces to viscous forces).
2) (35 points) It is a common practice when examining a fluid's viscous behavior to plot the shear strain rate (velocity gradient) dv dy on the abscissa versus shear stress (t) on the ordinate. When a fluid has a straight-line behavior between these two variables it is called a Newtonian fluid, and the resulting relationship is where u is the fluid viscosity. Many common fluids follow this behavior such as water, milk, and oil. Fluids that do not behave in...
Question 1: Derive an expression for the shear stress at the pipe wall when an incompressible fluid flows through a pipe under pressure. Use dimensional analysis with the following significant parameters: pipe diameter D, flow velocity V, fluid viscosity u and density, p of the fluid.