1 Discuss briefly the applicability of the Euler's equation. 2 Is Bernoulli equation valid in the...
Please answer the most questions you can. 1 Which terms in the Navier-Stokes equations are neglected in the Euler's equation? Discuss briefly the applicability of the Euler's equation. 2 Is Bernoulli equation valid in the boundary layers? Why? 3 In the Buckingham Pi theorem procedure, If we choose 3 repeating parameters (8%) (6%) and in total there are 6 dimensional parameters, then, how many nondimensional (696) parameters will show in the final functional relation f(?) 4 In chapter 7, when...
Problem 1 (15 points): Briefly discuss the simplifications to the Navier-Stokes equations to reduce to Couette flow. What assumptions allow you to cancel each term (be specific: relate each canceled term to a specific assumption/restriction)? Why wouldn't you be able to do this for turbulent flow?
Part B: Start with the 2-D Cartesian Navier-Stokes equations, explain which terms you can cross and why. Write the obtained differential equation and solve it with the given boundary conditions. Assume that two plates move in the same direction and U-0.5U1 Obtain velocity distribution between the plates.
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 =...
Task 9 4 Pts A flow of two layers of immiscible liquids is flowing through a channel. The flow is stationary, fully developed and laminar. Name the boundary conditions which have to be assumed at boundary 1 (water/tube), boundary 2 (water/oil) and boundary 3 (oil/air) to solve Navier Stokes equation. (See Fig 1) Sketch the velocity profiles in the two liquids. 3 air 2 oil 1 water Fig 1
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...
2. a) List the characteristics of turbulent flows and state why they are challenging to compute. [12 Marks b) The Navier-Stokes equations in two-dimensions for an incompressible fluid are given in part b) of Q1 above. When studying turbulent flows it is usual to time average these equations. Explain the process of time averaging and show which additional terms result from the time averaging process in two-dimensions for an incompressible fluid. 12 Marks c) When modelling turbulent flows the Navier-Stokes...
Question (1) A- Write full Navier Stokes equation and energy equation in cylindrical coordinates. From this derive equation for asymmetrical coordinates. Explain reasons for each assumption that you make while deriving the equation. B- Develop a relation for velocity and temperature distribution in a circular pipe which is experiencing a constant pressure gradient and a constant wall temperature. Explain each boundary condition
1) The Bernoulli equation is valid for inviscid flow. What term(s) in the energy balance are assumed to be zero? 2) A glass full of water placed on a standard kitchen scale weighs 0.7 Kg. If the scale is placed on the bottom of a swimming pool with the same glass on it, will the scale measure more or less than 0.7 kg. Explain your answer.
(Bernoulli Equations) Let p, f : I → R be continous functions defined on an interval I of R. Then for every α є R\ {0, 1), the 1st-order differential equation is called Bernoulli equation. It is a nonlinear ordinary differential equation. (a) Use the literature and describe in brief steps a method to find a solution of equation (1) Hint: See Trench, p.63 (b) Find all solutions to the following two differential equations. Use Mathematica to plot a direction...