A 2D steady, incompressible and inviscid flow field is defined by the velocity vector components: i)...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
A 2D steady, incompressible and inviscid flow field is defined by the velocity vector components: i) ii) i) u=-2xy ii) v=y² - x² Determine if the flow is irrotational? Problem T7.2 A 2D steady, incompressible and inviscid flow field is described by the velocity potential function: d=xy Determine the velocity field (u=? and v=?) Show that the continuity is satisfied. Attempt to sketch the constant value potential lines for the flow. Hint: For any constant value of C (where i=0 to n), sketch y=₁/x on X-Y plane. Remember: At any point (x,y), the velocity vector is normal to the potential line passing through (x,y). Determine the velocity potential function for this flow. Let at the origin(x=0, y=0). Equations: Angular velocity: Problem: T7.1 W₁ = w=0.0 1/dv ди əx ду - Definition of the velocity potential function , Problem: T7.2 dø dø 11 = and W= dø dz Problem T9.1 For the experimental data below, determine Average velocity 1 72 ū(x, y) == "undt = ¹ A -Źu, At Time (s) Velocity u (m/s) u= u - ū ú² = (u - ū)² Problem T9.2 Cp = Pe - Pt Pot Pt 1 nt - 1.2 10.3 10.0 1.4 Intensity of turbulence b) Determine the value of C 1= 4(u'² ū 1.6 1.8 Where, e refers to the diffuser exit and t for the diffuser inlet (throat). 'p, frictionless ' 2.0 10.1 10.4 10.0 10.2 9.9 2.2 Turbulence energy 2.4 1 k=(u)² 2.6 10.1 9.8 Total pressure: quantities u=? ú≈ 0 a) For an inviscid, steady and incompressible diffuser flow (thus, Bernoulli flow energy equation is valid) obtain the expression for the pressure recovery coefficient: -2 Cp, frictionless = 1- c) Can you achieve this theoretical value in the application? Give reasons why not? ܕܐܐܐ Po = P + + pv² if the velocity ratio between the inlet and exit is 5. Ç Problem T9.3 a) For a given steady flow, these are the values observed at a point in the flow. Total Acceleration in x direction= 5 (N/m³) Pressure gradient in X direction= -8 (N/m³) . ● Determine: du dt . b) At another location of the flow, if there is no acceleration, but the pressure gradient is still the same of -8 (N/m³) du dt Viscous (shear) force = ? (N/m³) c) Consider a), if the flow is inviscid, what is the pressure gradient (?) to achieve the same total acceleration of 5 (N/m³) ? Determine: ● Viscous (shear) force = ? (N/m3) d) Consider the inviscid flow of c), and justify whether in the direction of flow the flow area remains constant or it is increasing or decreasing. Equations ди at др dx + u + μ ди Əx +v ди +w ổn ổn ổn + Oz² + ox²oy² ди əz body +ΣF bo Acceleration in X direction (N/kg) Incompressible momentum equations in X direction N/m³ 3 A 2D steady, incompressible and inviscid flow field is defined by the velocity vector components: i) ii) i) u=-2xy ii) v=y² - x² Determine if the flow is irrotational? Problem T7.2 A 2D steady, incompressible and inviscid flow field is described by the velocity potential function: d=xy Determine the velocity field (u=? and v=?) Show that the continuity is satisfied. Attempt to sketch the constant value potential lines for the flow. Hint: For any constant value of C (where i=0 to n), sketch y=₁/x on X-Y plane. Remember: At any point (x,y), the velocity vector is normal to the potential line passing through (x,y). Determine the velocity potential function for this flow. Let at the origin(x=0, y=0). Equations: Angular velocity: Problem: T7.1 W₁ = w=0.0 1/dv ди əx ду - Definition of the velocity potential function , Problem: T7.2 dø dø 11 = and W= dø dz Problem T9.1 For the experimental data below, determine Average velocity 1 72 ū(x, y) == "undt = ¹ A -Źu, At Time (s) Velocity u (m/s) u= u - ū ú² = (u - ū)² Problem T9.2 Cp = Pe - Pt Pot Pt 1 nt - 1.2 10.3 10.0 1.4 Intensity of turbulence b) Determine the value of C 1= 4(u'² ū 1.6 1.8 Where, e refers to the diffuser exit and t for the diffuser inlet (throat). 'p, frictionless ' 2.0 10.1 10.4 10.0 10.2 9.9 2.2 Turbulence energy 2.4 1 k=(u)² 2.6 10.1 9.8 Total pressure: quantities u=? ú≈ 0 a) For an inviscid, steady and incompressible diffuser flow (thus, Bernoulli flow energy equation is valid) obtain the expression for the pressure recovery coefficient: -2 Cp, frictionless = 1- c) Can you achieve this theoretical value in the application? Give reasons why not? ܕܐܐܐ Po = P + + pv² if the velocity ratio between the inlet and exit is 5. Ç Problem T9.3 a) For a given steady flow, these are the values observed at a point in the flow. Total Acceleration in x direction= 5 (N/m³) Pressure gradient in X direction= -8 (N/m³) . ● Determine: du dt . b) At another location of the flow, if there is no acceleration, but the pressure gradient is still the same of -8 (N/m³) du dt Viscous (shear) force = ? (N/m³) c) Consider a), if the flow is inviscid, what is the pressure gradient (?) to achieve the same total acceleration of 5 (N/m³) ? Determine: ● Viscous (shear) force = ? (N/m3) d) Consider the inviscid flow of c), and justify whether in the direction of flow the flow area remains constant or it is increasing or decreasing. Equations ди at др dx + u + μ ди Əx +v ди +w ổn ổn ổn + Oz² + ox²oy² ди əz body +ΣF bo Acceleration in X direction (N/kg) Incompressible momentum equations in X direction N/m³ 3
Expert Answer:
Related Book For
Vector Mechanics for Engineers Statics and Dynamics
ISBN: 978-0073212227
8th Edition
Authors: Ferdinand Beer, E. Russell Johnston, Jr., Elliot Eisenberg, William Clausen, David Mazurek, Phillip Cornwell
Posted Date:
Students also viewed these mechanical engineering questions
-
A two-dimensional incompressible flow field is defined by the velocity components where V and L are constants, if they exist, find the stream function and velocity potential.
-
QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...
-
- The first stream is $450 per year for 9 years and begins 5 years from today - The second stream begins 7 years from today with the first cash flow being $400, and with each successive cash flow...
-
Match the geometric sequence with its graph. [The graphs are labeled (a), (b), (c), and (d).] (a) (b) (c) (d) 1. an = 18(2 / 3)n-1 2. an = 18(-2 / 3)n-1 3. an = 18 (3 / 2)n-1 4. an = 18(- 3 / 2)n-1...
-
Consider the stock and bond lattices on the left of Figure 14.18. Each has unit cost of \(\$ 1\) with the payoffs shown at the end nodes. There is a new asset available-a derivative of the first two...
-
Determine the largest length of a structural A-36 steel rod if it is fixed supported and subjected to an axial load of \(100 \mathrm{kN}\). The rod has a diameter of \(50 \mathrm{~mm}\). Use the AISC...
-
Dash Incorporated has the following convertible bond outstanding: Coupon ........5% Principal ........$1,000 Maturity ........12 years Conversion price ...$33.34 Conversion ratio ...30 shares Call...
-
Bonita Inc. had a bad year in 2019. For the first time in its history, it operated at a loss. The company's income statement showed the following results from selling 76,000 units of product: net...
-
It is December of 2020 and Frankie and Kensley Nguyen have come to you to discuss their 2020 tax situation and some changes they are proposing for the future. They are a married couple and have no...
-
Distinguish between demand and quantity demanded. Indicate how each of the following factors will change the individual demand curve for aspirin tablets: an increase in income an increase in the...
-
How can business writers ensure their documents are accessible to a diverse audience, including individuals with disabilities or those who speak English as a second language, without compromising on...
-
Give the number of protons and neutrons in the nucleus of each of the following isotopes. (a) fluorine20 protons and neutrons (b) aluminum25 protons and neutrons (c) tin120 protons and neutrons (d)...
-
A large statue, with a mass of 180 kg, is lifted through a height of 2.33 m onto a display pedestal. It is later lifted from the pedestal back to the ground for cleaning. a) Calculate the work done...
-
Examine the role of storytelling in business writing. How can this technique be leveraged to create engaging and relatable content for internal and external audiences, and what are the potential...
-
A system consists of 10^4 particles and 3 energy levels (E0 = 0, E1 = hv, and E2 = 2 hv). The total available energy, Etot, is 5000 hv. Constraints: Etot = const. and Ntot = const. What is the...
-
The following is the income statement of XXX Company as of 31 December 2016: For the period from 1 January 2016 till 31 December 2016 Note L.E. Services /commission revenues 2,882,451 Cost of...
-
Huntingdon Capital Corp. is a competitor of Plazacorp and First Capital Realty. Huntingdon reported the following selected information (in millions):...
-
Locate the centroid of the plane area shown. 90 mm 90 mm 120 mm Elliptical spandrel
-
A drum of 100-mm radius is attached to a disk of 200-mm radius. The disk and drum have a combined mass of 5 kg and a combined radius of gyration of 150 mm. A cord is attached to the drum at A and...
-
A small rivet connecting two pieces of sheet metal is being clinched by hammering. Determine the impulse exerted on the rivet and the energy absorbed by the rivet under each blow, knowing that the...
-
Last year during the week of July 4th, Murrysville Regional Hospital reported that they treated 264 patients for fireworks-related injuries.
-
The number of stores a person visits on a shopping trip Name and define the four types of measurement levels used in statistics. determine whether the data are qualitative or quantitative.
-
During a recent year, the average U.S. diners spent a month on food prepared outside the home was \($144\) . What is meant by a biased sample? determine whether descriptive or inferential statistics...
Study smarter with the SolutionInn App