Fox And Mcdonald's Introduction To Fluid Mechanics
9th Edition
ISBN: 9781118921876
Author: Pritchard, Philip J.; Leylegian, John C.; Bhaskaran, Rajesh
Publisher: WILEY
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Chapter 2, Problem 18P
Consider the flow described by the velocity field
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1. For a two-dimensional, incompressible flow, the x-component of velocity is given by u = xy2 . Find the simplest y-component of the velocity that will satisfy the continuity equation. 2. Find the y-component of velocity of an incompressible two-dimensional flow if the x-component is given by u = 15 − 2xy. Along the x-axis, v = 0.
Fluid Mechanics
Assis.Professor Dr. Hasan Ali Jurmut
HOMEWORK
Q/A two-dimensional flow field has velocities along the x and y
directions given by u = x2t and v = 2xyt, respectively, wheret is time.
Determine the acceleration .If the time is(5 sec.) at point (3,5).
Q/Consider steady, incompressible and flow through a reducer in a
horizontal pipe where the diameter is reduced from 20 cm to 10 cm. The
pressure in the 20 cm and 10cm is 150 and 50 kPa respectively. Compute the
flow rate in m²/s.
2
150 kPa
50 kPa
V,
V,
10 cm
20 cm
20 cm
II
Given a velocity field as
V(x, y, z) = axî – ayĵ
%3D
With units of velocity in m/sec; x and y in meters; and the constant
coefficient a = 0.1 sec.
a) Determine the equation for the streamline passing through the point
(x, y, 0) = (2, 8, 0).
b) Determine the velocity of a particle at the point (2, 8, 0).
c) If we mark the particle passing through the point (xo, Yo, 0) at to = 0,
determine the location of the particle at time t = 20 sec.
d) Show that the equation of the particle path (the pathline) matches the
equation of the streamline.
Chapter 2 Solutions
Fox And Mcdonald's Introduction To Fluid Mechanics
Ch. 2 - For the velocity fields given below, determine:...Ch. 2 - For the velocity fields given below, determine:...Ch. 2 - A viscous liquid is sheared between two parallel...Ch. 2 - For the velocity field V=Ax2yi+Bxy2j, where A = 2...Ch. 2 - A fluid flow has the following velocity...Ch. 2 - When an incompressible, nonviscous fluid flows...Ch. 2 - For the free vortex flow the velocities are t =...Ch. 2 - For the forced vortex flow the velocities are t =...Ch. 2 - A velocity field is specified as V=axyi+by2j,...Ch. 2 - A velocity field is given by V=ax3i+bxy3j, where a...
Ch. 2 - The velocity for a steady, incompressible flow in...Ch. 2 - The flow field for an atmospheric flow is given by...Ch. 2 - For the velocity field V=AxiAyj,, where A = 2s 1....Ch. 2 - A velocity field in polar coordinates is given...Ch. 2 - The flow of air near the Earths surface is...Ch. 2 - A velocity field is given by V=aytibxj, where a =...Ch. 2 - Air flows downward toward an infinitely wide...Ch. 2 - Consider the flow described by the velocity field...Ch. 2 - Consider the velocity field V = axi + by(1 + ct)...Ch. 2 - Consider the flow field given in Eulerian...Ch. 2 - A velocity field is given by V=axti+byj, where A =...Ch. 2 - Consider the garden hose of Fig. 2.5. Suppose the...Ch. 2 - Consider the velocity field of Problem 2.18. Plot...Ch. 2 - Streaklines are traced out by neutrally buoyant...Ch. 2 - Consider the flow field V=axti+bj, where a = 1/s2...Ch. 2 - A flow is described by velocity field V=ay2i+bj,...Ch. 2 - Tiny hydrogen bubbles are being used as tracers to...Ch. 2 - A flow is described by velocity field V=ai+bxj,...Ch. 2 - A flow is described by velocity field V=ayi+btj,...Ch. 2 - A flow is described by velocity field V=ati+bj,...Ch. 2 - The variation with temperature of the viscosity of...Ch. 2 - The variation with temperature of the viscosity of...Ch. 2 - Some experimental data for the viscosity of helium...Ch. 2 - The velocity distribution for laminar flow between...Ch. 2 - What is the ratio between the viscosities of air...Ch. 2 - Calculate velocity gradients and shear stress for...Ch. 2 - A very large thin plate is centered in a gap of...Ch. 2 - A female freestyle ice skater, weighing 100 lbf,...Ch. 2 - A block of mass 10 kg and measuring 250 mm on each...Ch. 2 - A 73-mm-diameter aluminum (SG = 2.64) piston of...Ch. 2 - A vertical gap 25 mm wide of infinite extent...Ch. 2 - A cylinder 8 in. in diameter and 3 ft long is...Ch. 2 - Crude oil at 20C fills the space between two...Ch. 2 - The piston in Problem 2.40 is traveling at...Ch. 2 - A block of mass M slides on a thin film of oil....Ch. 2 - A block 0.1 m square, with 5 kg mass, slides down...Ch. 2 - A torque of 4 N m is required to rotate the...Ch. 2 - A circular disk of diameter d is slowly rotated in...Ch. 2 - The fluid drive shown transmits a torque T for...Ch. 2 - A block that is a mm square slides across a flat...Ch. 2 - In a food-processing plant, honey is pumped...Ch. 2 - SAE 10W-30 oil at 100C is pumped through a tube L...Ch. 2 - The lubricant has a kinematic viscosity of 2:8105...Ch. 2 - Calculate the approximate viscosity of the oil....Ch. 2 - Calculate the approximate power lost in friction...Ch. 2 - Fluids of viscosities 1 = 0.1 Ns/m2 and 2 = 0.15...Ch. 2 - A concentric cylinder viscometer may be formed by...Ch. 2 - A concentric cylinder viscometer is driven by a...Ch. 2 - A shaft with outside diameter of 18 mm turns at 20...Ch. 2 - A shock-free coupling for a low-power mechanical...Ch. 2 - A proposal has been made to use a pair of parallel...Ch. 2 - The cone and plate viscometer shown is an...Ch. 2 - A viscometer is used to measure the viscosity of a...Ch. 2 - A concentric-cylinder viscometer is shown. Viscous...Ch. 2 - Design a concentric-cylinder viscometer to measure...Ch. 2 - A cross section of a rotating bearing is shown....Ch. 2 - Small gas bubbles form in soda when a bottle or...Ch. 2 - You intend to gently place several steel needles...Ch. 2 - According to Folsom [6], the capillary rise h...Ch. 2 - Calculate and plot the maximum capillary rise of...Ch. 2 - Calculate the maximum capillary rise of water...Ch. 2 - Calculate the maximum capillary depression of...Ch. 2 - Water usually is assumed to be incompressible when...Ch. 2 - The viscous boundary layer velocity profile shown...Ch. 2 - In a food industry process, carbon tetrachloride...Ch. 2 - What is the Reynolds number of water at 20C...Ch. 2 - A supersonic aircraft travels at 2700 km/hr at an...Ch. 2 - SAE 30 oil at 100C flows through a 12-mm-diameter...Ch. 2 - A seaplane is flying at 100 mph through air at...Ch. 2 - An airliner is cruising at an altitude of 5.5 km...
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- Velocity field of an incompressible flow is given by V = 6xi − 6yj (m/s) a) Find the pathlines in x-y plane. Make a sketch of pathlines for x ≥ 0 and y ≥ 0. b) Find the streamlines. Make a sketch of streamlines for x ≥ 0 and y ≥ 0. c) At time t = 0 s, the position of a rectangular fluid element ABCD is described by the corner points A(1,3), B(2,3), C(1,2) and D(2,2). Determine the new position of the fluid element at time t = 1/6 sarrow_forwardFor a given hypothetical flow the velocity at time t = 0 to t = 10 s was u = 0, v = 4m/s. Then from time t = 10 s to t = 15 s, the velocity was u = - 2 m/s, v = 2 m/s. A dye streak was started at a point in the flow field at time t = 0, and the path of a particle in the fluid was also traced. Draw to scale the streakline, pathline of the particle and streamlines at t = 15 s.arrow_forward1-Consider the flow of a fluid in rectangular coordinates VX=XY2, VY=-X2Y, VZ=0 and ρ=xy. Make sure the velocity and density represent a physically possible flow. Remarks: For resolution, use the continuity equation. Furthermore, it is important to look in the literature for what flow is possible from the continuity equation together with the substitution of rectangular coordinate values.arrow_forward
- A flow is described by velocity field, V=ayi+btj, where a=1 s-1and b=0.5 m/s2.At t=n s (Where n is 19), what are the coordinates of the particle that passed through point (1,2) at t=n-1? At t=n+1 s, what are the coordinates of the particle that passed through point (1,2) at t=n+1 s? Plot the pathline and streakline through point (1,2) and compare with the streamlines through the same point at the instants t=n-1 , n and n+1 s.arrow_forwardThe stream function relation is given as: Y = xy Find the equations for the components of velocity. Check if we satisfy continuity. Also, plot streamlines for a constant y=4 and y=1.arrow_forwardFlow 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_forward
- Give the solution fast in 30 minarrow_forwardy = 2r'sin20 (2) 0.5 m A 20 inviscid incompressible In addition, if Y=1, draw a streamline. Also plot some polar coordinates (r, 0) passing through the streamline, and indicate the direction of the velocity fluid flow around a corner is described by the stream function as shown. The fluid density is 1000kg/m3, and the plane is horizontal, determine the velocity potential. If the pressure at (1) is 30 kPa, what the pressure at (2)? vector.arrow_forward1. Find the stream function for a parallel flow of uniform velocity V0 making an angle α with the x-axis. 2. A certain flow field is described by the stream function ψ = xy. (a) Sketch the flow field. (b) Find the x and y velocity components at [0, 0], [1, 1], [∞, 0], and [4, 1]. (c) Find the volume flow rate per unit width flowing between the streamlines passing through points [0, 0] and [1, 1], and points [1, 2] and [5, 3].arrow_forward
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