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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Chapter 6, Problem 70P
The velocity field for a two-dimensional flow is
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The velocity field for an incompressible flow is given by V = 5x ^ 2i- 20 xyj + 100tk. Explain whether this flow is steady or not. Is the flow two or three dimensional? Determine the magnitude and direction of the velocity and acceleration of a flow particle at t = 0.2 and position (1, 2, 3).
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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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- Flow through a converging nozzle can be approximated by a one-dimensional velocity distribution u=vo (1+2). For the nozzle shown below, assume that the velocity varies linearly from u = vo at the entrance to u = 3v, at the exit. Compute the acceleration at the entrance and exit if vo=10m/s and L = 1m. x=0 X u= :326 x=Larrow_forwardDo all three parts of problemarrow_forwardAn incompressible frictionless flow field is given by V = (Ax + By)i + (Bx – Ay)j where A 1 s1 and B = 3 st, and x and y are in meters. The fluid is water and gravitational %D acceleration = 9.81 m/s? in the y-direction. (a) Determine the magnitude and direction of the acceleration vector (b) Determine the pressure gradients in both x- and y-directions at (x, y) = (2, 2) Hint: use Euler's Equation to determine pressure gradients.arrow_forward
- A fluid has a velocity field defined by u = x + 2y and v = 4 -y. In the domain where x and y vary from -10 to 10, where is there a stagnation point? Units for u and v are in meters/second, and x and y are in meters. Ox = 2 m. y = 1 m x = 2 m, y = 0 No stagnation point exists x = -8 m, y = 4 m Ox = 1 m, y = -1 m QUESTION 6 A one-dimensional flow through a nozzle has a velocity field of u = 3x + 2. What is the acceleration of a fluid particle through the nozzle? Assume u, x and the acceleration are all in consistent units. O 3 du/dt 9x + 6 1.5 x2 + 2x O Oarrow_forwardConsider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and v = 2yt. Do the fluid elements experience angular rotation? Thus, state whether the flow field is rotational or irrotational.arrow_forwardWater is flowing in a circular pipe of varying cross-sectional area. At one point in the pipe the radius of the pipe is 0.2 m. What must be the water velocity at this point if the volume velocity o water is 0.8 m³.s^-1? Hint: Use continuity equation.arrow_forward
- The velocity of a flow is given as V = -x² i + (x + 2y) j. where V is in ft/s and X and y are in ft. • What is the volumetric strain rate at X = 0, y = 0? • What is the vorticity at X = 0, y = 0? Air at 80° C and standard atmospheric pressure flows through a round pipe 40 cm in diameter at a speed of 9 m/s. • What is the mass flow rate of this air flow? • What is the specific kinetic energy in this flow?arrow_forward1. For a flow in the xy-plane, the y-component of velocity is given by v = y2 −2x+ 2y. Find a possible x-component for steady, incompressible flow. Is it also valid for unsteady, incompressible flow? Why? 2. The x-component of velocity in a steady, incompressible flow field in the xy-plane is u = A/x. Find the simplest y-component of velocity for this flow field.arrow_forwardA two-dimensional incompressible velocity fi eld has u =K (1 - e - ay ), for x ≤ L and 0 ≤ y ≤ ∞. What is the mostgeneral form of υ ( x , y ) for which continuity is satisfi edand υ = υ 0 at y= 0? What are the proper dimensions forconstants K and a ?arrow_forward
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