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 2, Problem 10P
A velocity field is given by
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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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- Please answers in detail solutionarrow_forwardThe components of a two-dimensional velocity field are u = 4 + y³ and v = 16. The equation for a streamline can be written as y++ Ay + Bx + C = 0. Determine the values of the coefficients for the streamline passing through (3, 1). A = i B = i C= iarrow_forwardConsider the velocity field represented by V = K (yĩ + xk) Rotation about z-axis isarrow_forward
- An unsteady velocity field V = xy^2ti + zxj −t^3k exists at the 3D plane along a streamline that passes through the point (3,-1,2) at t = 0. Find the equation representing this streamline.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_forwardQuestion 4: The velocity field of a flow is given by V = axyi + by'j where a = 1 m's' and b = - 0.5 m's". 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 plane (2.arrow_forward
- This problem will show you how to obtain the pathline and the streamline for a velocity field. A velocity field is given by u=(ax_1 t)i −(bx_2)j , where a=0.1^s−2 and b=1s^−1. (a) For the particle that passes through the point (x1,x2) = (1,1) at instant t = 0, get the equation of the pathline during the interval from t = 0 to t = 3s. Plot it roughly by hand(b) Get the equations of the streamlines through the same point at the instants t = 0,1, and 2s. Plot it roughly by handarrow_forward1. For a velocity field described by V = 2x2i − zyk, is the flow two- or threedimensional? Incompressible? 2. For an Eulerian flow field described by u = 2xyt, v = y3x/3, w = 0, find the slope of the streamline passing through the point [2, 4] at t = 2. 3. Find the angle the streamline makes with the x-axis at the point [-1, 0.5] for the velocity field described by V = −xyi + 2y2jarrow_forwardcomplete and readable solutionarrow_forward
- 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_forwardExample 10.4-1 Stream Functions for a Flow Field The velocity components for a flow field are as follows: v, = a(x² – y²³), v, =-2axy V. V. %3D Prove that it satisfies continuity equation for two dimensional flows and find y. Plot streamlines for y=1 to y=6.arrow_forwardA 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_forward
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