Fox And Mcdonald's Introduction To Fluid Mechanics
9th Edition
ISBN: 9781118921876
Author: Pritchard, Philip J.; Leylegian, John C.; Bhaskaran, Rajesh
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 6, Problem 83P
A source with a strength of q = 3π m2/s and a sink with a strength of q = π m2/s are located on the x axis at x = −1 m and x = 1 m, respectively. Determine the stream function and velocity potential for the combined flow and sketch the streamlines.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A horizontal flow field has the following velocity components:
= (y² – x²) m/s
=
v = (2xy) m/s
a) The pressure at point A (3m,2m) is 600 kPa. Calculate the pressure at point B
(1m,3m).
b) Determine the potential function for the flow.
Use y = 8kN/m3
16°C
for the following flows, find the equation of the streamline through(1,1). v= -y^(2)i-6xj
Q3
The stream function for a given 2D flow fields is
V = 5a²y – (s/3)y
Determine the corresponding velocity potential.
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
- Determine the two-dimensional stream function corresponding to o = Aln(r/ro), where A is a constant. What is the flow pattern? Plot the velocity field, potential field, and 3. streamlinesarrow_forward1. Find the velocity field, and volumetric flowrate between two plates ofwidth W and separation distance H when the bottom plate is heldfixed and the top plate is pulled to the right with velocity V . Also findthe force necessary to push the top plate. 2. Now hold both plates stationary, but impose pressure p0 on the left endof the channel, and pressure p0 + ∆p (∆p > 0) on the right end of thechannel. Find the velocity field and volumetric flow rate. 3. What is the volumetric flow rate if you simultaneously move the topplate and impose the same pressure drop? 4. Lid-driven cavity flow is exactly this last situation, except that bothends of the channel are capped off, and the pressure drop is not imposed, but rather arises from the sliding of the lid combined with beingenclosed. What is the pressure drop that arises?arrow_forwardThe two-dimensional flow of a nonviscous, incompressible fluid in the vicinity of the 90° corner is described by the potential velocity = 4r²cos20. Take a density 1000 kg/m³ and determine, if possible, the corresponding stream function and the pressure at point 1 on the wall is 50kPa. What is the pressure at point 2? 51 0.5 m 2arrow_forward
- A fluid of density ρ and viscosity μ flows from left to right through the horizontal pipe of radius a and lengthL, shown in the figure below. The pressures at the centers of the inlet and exit are P1 and P2 ,respectively. You may assume that the only non-zero velocity component is vz and that it is not afunction of the angular coordinate, θ.(a) Simplify the continuity equation and show that vz = vz(r), i.e., it is a function of r only.(b) Simplify the momentum balance equation in the z-direction and show that it equals equation a in the image (c) Assuming that (dP/dz)=-delta P/L , solve the above equation with appropriate boundaryconditions and show that it equals equation c in the image(d) Show that the volumetric flow rate equals equation d in the imagearrow_forwardSources of equal strength m are placed at the four symmetricpositions (x, y) = (a, a), (-a, a), (-a, -a), and (a, -a).Sketch the streamline and potential line patterns. Do anyplane “walls” appear?arrow_forwardThe velocity field of a flow is given by V= axyi + by^2j where a = 1 m^-1s^-1 and b = - 0.5 m^-1s^-1. The coordinates are in meters. Determine whether the flow field is three-, two-, or one-dimensional. Find the equations of the streamlines and sketch several streamlines in the upper half planearrow_forward
- The flow of an incompressible §uid is defined by u=3, v=9x. Does a stream function exist for this flow? If so, determine the expression for the stream function,Ψ.arrow_forwardWhat is the flow pattern? Plot the velocity field, potential field, and streamlines. Please explain it in detail.arrow_forwardConsider the flow field V = (ay+dx)i + (bx-dy)j + ck, where a(t), b(t), c(t), and d(t) are time dependent coefficients. Prove the density is constant following a fluid particle, then find the pressure gradient vector gradP, Γ for a circular contour of radius R in the x-y plane (centered on the origin) using a contour integral, and Γ by evaluating the Stokes theorem surface integral on the hemisphere of radius R above the x-y plane bounded by the contour.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