Fox and McDonald's Introduction to Fluid Mechanics
9th Edition
ISBN: 9781118912652
Author: Philip J. Pritchard, John W. Mitchell
Publisher: WILEY
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Textbook Question
Chapter 6, Problem 11P
The velocity field for a plane vortex sink is given by
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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...
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- Determine whether each of the followings are rotational flow or irrotational flow. Also, determine their stream functions. (u: x-component of velocity. v: y-component of velocity.) 1. u=x^3-3(x)(y^2), v=y^3-3(x^2)(y) 2. u=2xy, v=-y^2arrow_forwardThe 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?arrow_forwardThe 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.arrow_forward
- The 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_forwardThe 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_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_forward
- for the following flows, find the equation of the streamline through(1,1). v= -y^(2)i-6xjarrow_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_forwardConsider the velocity field given by u = y/(x2 + y2) and v = −x/(x2 + y2). Calculate the equation of the streamline passing through the point (0, 5).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_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_forwardIt is given as u = 2 (1 + t), v = 3 (1 + t), w = 4 (1 + t) in a flow field. Accordingly, find the velocity and acceleration values at the points (3,2,4) at t=2 seconds.arrow_forward
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