Question: 1. Consider a liquid placed between two infinite planar plates. The plates are oriented perpendicular to the gravitational acceleration g and the liquid is

1. Consider a liquid placed between two infinite planar plates. The plates are oriented perpendicular to the

1. Consider a liquid placed between two infinite planar plates. The plates are oriented perpendicular to the gravitational acceleration g and the liquid is at rest. At t = 0, one plate at z = 0 is suddenly moved in the x direction with the constant speed U, while the top plate at z = d is kept fixed in the laboratory. a) Simplify Navier-Stokes equation for this system and obtain boundary and initial conditions. (10)+ b) What are characteristic velocity and length? Non-dimensionalize the governing equation and obtain characteristic time. What is new boundary and initial conditions? Are the conditions are homogeneous? (10) c) Obtain steady-state solution for velocity profile. (10)+ d) Define transient solution as difference of unsteady velocity profile from steady-state velocity profile and obtain new equation and conditions. Are the conditions are homogeneous? (10) e) Solve the equation with conditions and obtain the equation for unsteady velocity profile. (15) f) For water in two plates with separation of 1 cm and pulling velocity U= 1 cm/s, plot the profiles at five different times (select the times which show different profiles from each other). (15)

Step by Step Solution

★★★★★

3.40 Rating (172 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a The NavierStokes equation for this 2D system is ut uux vuz 1 Px 2ux2 2uz2 vt uvx vvz 1 Pz 2vx2 2v... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Accounting Questions!

Oakey Wines has the option to lease a filling machine for the bottling of exclusive varieties that are sold in smaller volumes and require unique bottles. There are 3 options available to Oakey...

5. [5] State g(n)'s runtime complexity: int f(int n){+ if(n

a. Example 13-1: Batch Reactor with an Exothermic Reaction Wolfram 1. Adiabatic Case: Use Wolfram to see whether you can find a trajectory that is ready to ignite and whose trajectory looks like a...

Pls answer all the questions step by step and show the workings clearly.Thank you! All info there pls check again 1. 2. 3. A8 How do two point charges that interact through Coulomb's law \"know\"...

Please help Asap with grade 12 student knowledge and show step-by-step. Thank you. Q#2. A charged small plastic bead is suspended under the center of a smooth charged plate (see below in part (a) --...

3. [1pt] Aww A charge q is moving with initial velocity of through a uni- form magnetic field that points out of the page. The figure below shows six possible paths that the charge might take. 1 4 2...

You have a channel system in which the water flows through and is bounded with two perforated plates at the bottom and the top. Consider steady, incompressible, laminar flow between two infinite...

please help Lesson 1: Magnetlc Fields 1. In the diagram below; a compass is placed under the conductor and the conductor is carrying conventional current from Ate B. In which direction will the...

Answer the questions below about the effect of surface properties on materials processing. The "Laplace force", which acts to liquid as inner pressure to minimize surface area (or total surface...

The experimental result differs from the assumption. The result shows that the ring oscillator frequencies can be grouped into two groups, where the first group is the high frequency group for the...

What is the major weakness of the single-step form for the income statement?

Question The graph of f(x) = -x + ax +bx+c is sketched below. The x-intercepts are indicated. 11.1 11.2 11.3 0 A BI $ Calculate the values of a, b and c. Calculate the x-coordinates of A and B. the...

What is wrong with the view that it is cheaper to issue a bond with a warrant or a convertible feature because the required coupon is lower?

Thank you in advance for your help. I have made ANOVA tables from the data I was given and I have summarized it in the table below. Are these questions asking about the P-value as well? Or do I have...

18. . When the economy moves from Point C to Point A, there has been: an increase in quantity demanded and an increase in supply. O an increase in demand and an increase in supply. an increase in...

17. The above table gives the demand and supply schedules for Blu-ray discs. Based on the table, the equilibrium quantity and price of a Blu-ray discs is: 16,000 and $16 O 20,000 and S20 16,000 and...

7. According to the law of there is a positive relationship between price and supply; the quantity supplied supply; the change in supply O demand; change in demand O demand; quantity demanded

19. The above figure shows a graph of the market for pizzas in a large town. If the price increases from S7 to S8 per pizza, the quantity of pizzas demanded will: O decrease by 10. increase by 30...

how hard would it be analytically investigate the feasible region of the given need in the state of California

Find the general solution. Indicate which method in this chapter you are using. Show the details of your work. 25yy' - 4x = 0

Integrate f(z) counterclockwise around the unit circle. Indicate whether Cauchys integral theorem applies. Show the details. f(z) = 1/(4z - 3)

Is the matrix A Hermitian or skew-Hermitian? Find xÌ T Ax . Show the details. [2i -2 + 3i i 2 + 3i

Prove Eulers theorem that, if ( L , K ) is homogeneous of degree(see Exercise 5.7), then L ( / L )+ K ( f / K )= ( L , K ). Given this result, what can you conclude if a production function has...

The only variable input a janitorial service firm uses to clean offices is workers who are paid a wage, w, of $8 an hour. Each worker can clean four offices in an hour. Use math to determine the...

Replace the production function in Solved Problem 7.4 with a Cobb-Douglas q = AL a K b , and use calculus to find the cost minimizing capital-labor ratio?