Question: For fully developed laminar incompressible flow through a straight noncircular duct, as in Sec. 6.8, the Navier-Stokes Equation (4.38) reduce to where (y, z) is

For fully developed laminar incompressible flow through a straight noncircular duct, as in Sec. 6.8, the Navier-Stokes Equation (4.38) reduce to where (y, z) is the plane of the duct cross section and x is along the duct axis. Gravity is neglected. Using a non-square rectangular grid (Δx, Δy), develop a finite-difference model for this equation, and indicate how it may be applied to solve for flow in a rectangular duct of side lengths a and b.

For fully developed laminar incompressible

Il it it up const < 0 i-1.j+1 i+1j+1 Az 1.J i+1.j Ay Ay i-1j-1 ij-1 i+1j-1

Step by Step Solution

★★★★★

3.41 Rating (154 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

An appropriate square grid is shown above The finitedifference ... 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

Document Format (1 attachment)

E-ME-FM (1008).docx

120 KBs Word File

Students Have Also Explored These Related Mechanical Engineering Questions!

A propeller shaft of solid circular cross section and diameter d is spliced by a collar of the same material (see figure). The collar is securely bonded to both parts of the shaft. What should be the...

A steel bar of solid circular cross section and length L 2.5m is subjected to an axial tensile force T = 24kN and a bending moment M = 3.5kNm (see figure). (a) Based upon an allowable stress in...

For fully developed laminar flow through a parallel-plate channel, the x-momentum equation has the form (d 2 u/dy 2 ) = dp/dx = constant. The purpose of this problem is to develop expressions for the...

Fluid Dynamics a) b) c) d) e) g) . Consider a steady, fully developed, laminar, incompressible flow of water with constant properties (Density = 992 kg/m?, Kinematic viscosity = 6.6 x 10\"7 m?/s)...

Consider a steady, fully developed, laminar, incompressible flow of water with constant properties ( Density = 9 9 2 k g m 3 , Kinematic viscosity = 6 . 6 1 0 - 7 m 2 s ) between the parallel plates...

Answer the volumetric flow rate, Q (ft^3/s): 8.17 Benzene flows steadily and continuously at 100F through a 3000 -ft horizontal pipe with a constant diameter of 4 in. The pressure drop across the...

Benzene flows steadily and continuously at 100 F through a 3000-ft horizontal pipe with a constant diameter of 4 in. The pressure drop across the pipe under these conditions is 300 lbf/ft2. Assuming...

Benzene flows steadily and continuously at 100 F through a 3000-ft horizontal pipe with a constant diameter of 4 in. The pressure drop across the pipe under these conditions is 300 lb f /ft 2 ....

3.5 Benzene flows steadily and continuously at 100 through a 2000-ft horizontal pipe with a constant diameter of 4-in. The pressure drop across the pipe under these conditions is 300 lbf/ft2....

8.17 Benzene flows steadily and continuously at 100F through a 3000-ft horizontal pipe with a constant diameter of 4in. The pressure drop across the pipe under these conditions is 300 lbf/ft2....

In June 2009, the total population in the city of Calypso was 12,500. There were 10,000 non-institutionalized civilians that were eligible for the labor force. The civilian labor force was 8,000...

The articles on Blockchain and the dangers of investing in Digital Currencies (provided in this week's course material hereabove) and your own research,You will use your textbook, the university...

Describe and discuss the optimum moisture content for dead animal composting.

number 1 and 3 Transcript of Meeting with Anna, Omar, and Ted, and Peter Graff and Student on September 29, 2020 Anna: I feel so bad that we did not live up to our Dad's expectations and the company...

Surf Products Company uses an automated process to clean and polish its souvenir items. For March, the company had the following activities: Beginning work in process inventory 0 items Units placed...

64) For the geometry presented below, two walls are insulated (choppy lines) and the other one is exposed to convection. The geometry has been divided into nodes with a deltax = 1 mm and delta y = 4...

Emily Smith decides to buy a fuel-efficient used car. Here are several vehicles she is considering, with the estimated cost to purchase and the age of the vehicle. a. Plot these data on a scatter...

Sunland Company, opened an incorporated dental practice on January 1, 2022. During the first month of operations, the following transactions occurred. 1. Performed services for patients who had...

For each of the following independent situations, fill in the blanks to indicate the effect of the error on each of the various financial statement items. Indicate an understatement (U), an...

Goodwin Technologies, a relatively young company, has been wildly successful but has yet to pay a dividend. An analyst forecasts that Goodwin is likely to pay its first dividend three years from now....

Assume that a 3 -year Treasury security yields 4.50%. Also assume that the real risk-free rate (r) is 0.75%, and inflation is expected to be 2.25% annually for the next 3 years. In addition to...

Question 1 0 ( 1 point ) You have been asked to forecast Orwell's additional funds needed ( AFN ) for next year. Assuming the firm is operating at only 5 0 % of capacity and using the data in the...