Fox and McDonald's Introduction to Fluid Mechanics
9th Edition
ISBN: 9781118912652
Author: Philip J. Pritchard, John W. Mitchell
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 6, Problem 71P
A flow field is characterized by the stream function ψ = Axy, where A = 2 s−1 and the coordinates are measured in feet. Verify that the flow is irrotational and determine the velocity potential ϕ. Plot the streamlines and potential lines and visually verify that they are orthogonal.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
The expression for stream function is described by y = x ^ 3 - 3x * y ^ 2 . Indicate whether the flow is rotational or irrotational. Determine the value or velocity potential o, if it exists.
The velocity for the 2-dimensional flow is defined by V =(3y2 i+4xj) m/s, where y is in meters. Determine the equation of the streamline that passes through point (2 m, 1 m).
only HANDWRITTEN answer needed ( NOT TYPED)
1. The components of velocity in a flow field are given byu=x2+y2+z2v=xy+yz+z2w=-3xz- 0.5z2+4a) Determine the volumetric dilatation rate and interpret the result.b) Determine an expression for the rotation vector. Is this an irrotational flow field?
Chapter 6 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
Ch. 6 - An incompressible frictionless flow field is given...Ch. 6 - A velocity field in a fluid with density of 1000...Ch. 6 - The x component of velocity in an incompressible...Ch. 6 - Consider the flow field with the velocity given by...Ch. 6 - Consider the flow field with the velocity given by...Ch. 6 - The velocity field for a plane source located...Ch. 6 - In a two-dimensional frictionless, incompressible...Ch. 6 - Consider a two-dimensional incompressible flow...Ch. 6 - An incompressible liquid with a density of 900...Ch. 6 - Consider a flow of water in pipe. What is the...
Ch. 6 - The velocity field for a plane vortex sink is...Ch. 6 - An incompressible liquid with negligible viscosity...Ch. 6 - Consider water flowing in a circular section of a...Ch. 6 - Consider a tornado as air moving in a circular...Ch. 6 - A nozzle for an incompressible, inviscid fluid of...Ch. 6 - A diffuser for an incompressible, inviscid fluid...Ch. 6 - A liquid layer separates two plane surfaces as...Ch. 6 - Consider Problem 6.15 with the nozzle directed...Ch. 6 - Consider Problem 6.16 with the diffuser directed...Ch. 6 - A rectangular computer chip floats on a thin layer...Ch. 6 - Heavy weights can be moved with relative ease on...Ch. 6 - The y component of velocity in a two-dimensional...Ch. 6 - The velocity field for a plane doublet is given in...Ch. 6 - Tomodel the velocity distribution in the curved...Ch. 6 - Repeat Example 6.1, but with the somewhat more...Ch. 6 - Using the analyses of Example 6.1 and Problem...Ch. 6 - Water flows at a speed of 25 ft/s. Calculate the...Ch. 6 - Plot the speed of air versus the dynamic pressure...Ch. 6 - Water flows in a pipeline. At a point in the line...Ch. 6 - In a pipe 0.3 m in diameter, 0.3 m3/s of water are...Ch. 6 - A jet of air from a nozzle is blown at right...Ch. 6 - The inlet contraction and test section of a...Ch. 6 - Maintenance work on high-pressure hydraulic...Ch. 6 - An open-circuit wind tunnel draws in air from the...Ch. 6 - Water is flowing. Calculate H(m) and p(kPa). P6.36Ch. 6 - If each gauge shows the same reading for a flow...Ch. 6 - Derive a relation between A1 and A2 so that for a...Ch. 6 - Water flows steadily up the vertical 1...Ch. 6 - Your car runs out of gas unexpectedly and you...Ch. 6 - A tank at a pressure of 50 kPa gage gets a pinhole...Ch. 6 - The water flow rate through the siphon is 5 L/s,...Ch. 6 - Water flows from a very large tank through a 5 cm...Ch. 6 - Consider frictionless, incompressible flow of air...Ch. 6 - A closed tank contains water with air above it....Ch. 6 - Water jets upward through a 3-in.-diameter nozzle...Ch. 6 - Calculate the rate of flow through this pipeline...Ch. 6 - A mercury barometer is carried in a car on a day...Ch. 6 - A racing car travels at 235 mph along a...Ch. 6 - The velocity field for a plane source at a...Ch. 6 - A smoothly contoured nozzle, with outlet diameter...Ch. 6 - Water flows steadily through a 3.25-in.-diameter...Ch. 6 - A flow nozzle is a device for measuring the flow...Ch. 6 - The head of water on a 50 mm diameter smooth...Ch. 6 - Water flows from one reservoir in a 200-mm pipe,...Ch. 6 - Barometric pressure is 14.0 psia. What is the...Ch. 6 - A spray system is shown in the diagram. Water is...Ch. 6 - Water flows out of a kitchen faucet of...Ch. 6 - A horizontal axisymmetric jet of air with...Ch. 6 - The water level in a large tank is maintained at...Ch. 6 - Many recreation facilities use inflatable bubble...Ch. 6 - Water flows at low speed through a circular tube...Ch. 6 - Describe the pressure distribution on the exterior...Ch. 6 - An aspirator provides suction by using a stream of...Ch. 6 - Carefully sketch the energy grade lines (EGL) and...Ch. 6 - Carefully sketch the energy grade lines (EGL) and...Ch. 6 - Water is being pumped from the lower reservoir...Ch. 6 - The turbine extracts power from the water flowing...Ch. 6 - Consider a two-dimensional fluid flow: u = ax + by...Ch. 6 - The velocity field for a two-dimensional flow is...Ch. 6 - A flow field is characterized by the stream...Ch. 6 - The flow field for a plane source at a distance h...Ch. 6 - The stream function of a flow field is = Ax2y ...Ch. 6 - A flow field is characterized by the stream...Ch. 6 - A flow field is characterized by the stream...Ch. 6 - The stream function of a flow field is = Ax3 ...Ch. 6 - A flow field is represented by the stream function...Ch. 6 - Consider the flow field represented by the...Ch. 6 - Show by expanding and collecting real and...Ch. 6 - Consider the flow field represented by the...Ch. 6 - An incompressible flow field is characterized by...Ch. 6 - Consider an air flow over a flat wall with an...Ch. 6 - A source with a strength of q = 3 m2/s and a sink...Ch. 6 - The velocity distribution in a two-dimensional,...Ch. 6 - Consider the flow past a circular cylinder, of...Ch. 6 - The flow in a corner with an angle can be...Ch. 6 - Consider the two-dimensional flow against a flat...Ch. 6 - A source and a sink with strengths of equal...Ch. 6 - A flow field is formed by combining a uniform flow...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Consider the velocity field given by u = y/(x2 + y2) and v = −x/(x2 + y2). Calculate the vorticity.arrow_forwardθ(x,y)=x2-y2+2xy According to the potential equation of a two-dimensional flow in the horizontal plane defined as;1-) Is this current physically possible?2-) Determine the current function?3 -) Calculate the resultant velocity and resultant acceleration at the point (5,6).4 -) Calculate the flow rate passing between (2,2) and (3,3) streamlines.arrow_forwardFor the flow defined by the stream function ψ = V0y: (a) Plot the streamlines. (b) Find the x and y components of the velocity at any point. (c) Find the volume flow rate per unit width flowing between the streamlines y = 1 and y = 2.arrow_forward
- The velocity field is given as u=y-1 and v=y-2. The units of u and v are m/s and the units of x and y are meters. a) Draw the stream line passing through the point (x,y)=(4.3). b) Determine the streakline passing through the point (x, y) = (4,3) and compare it with the streamline. c) Determine whether the current is revolving or not.arrow_forwardIf the flow velocity is the same in magnitude and direction at every point in the fluid it is said to be a A. Transient Flow B. Steady FlowC. Unsteady Flow D. Uniform Flowarrow_forwardConsider the velocity field given by u = y/(x2 + y2) and v = −x/(x2 + y2). For the velocity field given , calculate the circulation around a circular path of radius 5 m. Assume that u and v given are in units of meters per second.arrow_forward
- Find the stagnation point in the following two-dimensional velocity field: V=(3+x-y)i + (5+x+y)jarrow_forward) The stream function for an incompressible flow field is given by the equation ψ=3x2y+y3 where the stream function has the units of with x and y in meters. (a) Sketch the streamline passing through the origin. (b) Determine the rate of flow across the straight path.arrow_forwardThe velocity components of an incompressible, two-dimensional field are given bythe following equations: u(x,y) =y^2 -x (1+x) v(x,y) = y(2x+1) Show that the flow field is (a) irrotational and (b) satisfies conservation of mass.arrow_forward
- According to the potential equation of a two-dimensional flow in the horizontal plane defined as; i-) Is this current physically possible? Prove ii-) Determine the current function ψ (x, y) of this current. [ψ (0,0) = 0] iii-) Calculate the resultant velocity and resultant acceleration at point A (e, f) in this flow field. iv-) Calculate the flow rate passing between the streamlines ψ (a, a) and ψ (c, c).arrow_forwardThe velocity vector in a flow is given by :V=-3xi-4yj-7zk Determine the stream equation passing through a point L(4,2,3)arrow_forwardConsider the flow field shown. Coordinates are measured in meters. For the particle that passes through the point ðx, yÞ = ð1, 2Þ at the instant t = 0, plot the pathline during the time interval from t = 0 to 3 s. Compare this pathline with the streakline through the same point at the instant t=3s.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Introduction to Kinematics; Author: LearnChemE;https://www.youtube.com/watch?v=bV0XPz-mg2s;License: Standard youtube license