FLUID MECHANICS FUNDAMENTALS+APPS
4th Edition
ISBN: 2810022150991
Author: CENGEL
Publisher: MCG
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Chapter 9, Problem 50P
Consider the channel flow of Fig. 9-45. The fluid is water at
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Chapter 9 Solutions
FLUID MECHANICS FUNDAMENTALS+APPS
Ch. 9 - Explain the fundamental differences between a flow...Ch. 9 - What does it mean when we say that two more...Ch. 9 - The divergence theorem is v.cdv=A c . n dACh. 9 - Prob. 4CPCh. 9 - Prob. 5CPCh. 9 - Prob. 6CPCh. 9 - Prob. 7PCh. 9 - Prob. 8PCh. 9 - Let vector G=2xzi12x2jz2kk . Calculate the...Ch. 9 - Prob. 10P
Ch. 9 - Prob. 11PCh. 9 - Prob. 12PCh. 9 - Prob. 13PCh. 9 - Alex is measuring the time-averaged velocity...Ch. 9 - Let vector c be given G=4xziy2i+yzkand let V be...Ch. 9 - The product rule can be applied to the divergence...Ch. 9 - Prob. 18PCh. 9 - Prob. 19PCh. 9 - Prob. 20CPCh. 9 - In this chapter we derive the continuity equation...Ch. 9 - Repeat Example 9-1(gas compressed in a cylinder by...Ch. 9 - Consider the steady, two-dimensional velocity...Ch. 9 - The compressible from of the continuity equation...Ch. 9 - In Example 9-6 we derive the equation for...Ch. 9 - Consider a spiraling line vortex/sink flow in the...Ch. 9 - Verify that the steady; two-dimensional,...Ch. 9 - Consider steady flow of water through an...Ch. 9 - Consider the following steady, three-dimensional...Ch. 9 - Consider the following steady, three-dimensional...Ch. 9 - Two velocity components of a steady,...Ch. 9 - Imagine a steady, two-dimensional, incompressible...Ch. 9 - The u velocity component of a steady,...Ch. 9 - Imagine a steady, two-dimensional, incompressible...Ch. 9 - The u velocity component of a steady,...Ch. 9 - What is significant about curves of constant...Ch. 9 - In CFD lingo, the stream function is often called...Ch. 9 - Prob. 39CPCh. 9 - Prob. 40CPCh. 9 - Prob. 41PCh. 9 - Prob. 42PCh. 9 - Prob. 44PCh. 9 - Prob. 45PCh. 9 - As a follow-up to Prob. 9-45, calculate the volume...Ch. 9 - Consider the Couette flow of Fig.9-45. For the...Ch. 9 - Prob. 48PCh. 9 - AS a follow-up to Prob. 9-48, calculate the volume...Ch. 9 - Consider the channel flow of Fig. 9-45. The fluid...Ch. 9 - In the field of air pollution control, one often...Ch. 9 - Suppose the suction applied to the sampling...Ch. 9 - Prob. 53PCh. 9 - Flow separates at a shap corner along a wall and...Ch. 9 - Prob. 55PCh. 9 - Prob. 56PCh. 9 - Prob. 58PCh. 9 - Prob. 59PCh. 9 - Prob. 60PCh. 9 - Prob. 61PCh. 9 - Prob. 62PCh. 9 - Prob. 63EPCh. 9 - Prob. 64PCh. 9 - Prob. 65EPCh. 9 - Prob. 66PCh. 9 - Prob. 68EPCh. 9 - Prob. 69PCh. 9 - Prob. 71PCh. 9 - Prob. 72PCh. 9 - Prob. 73PCh. 9 - Prob. 74PCh. 9 - Prob. 75PCh. 9 - Wht in the main distionction between Newtormine...Ch. 9 - Prob. 77CPCh. 9 - What are constitutive equations, and to the fluid...Ch. 9 - An airplane flies at constant velocity Vairplane...Ch. 9 - Define or describe each type of fluid: (a)...Ch. 9 - The general cool volume from of linearmomentum...Ch. 9 - Consider the steady, two-dimensional,...Ch. 9 - Consider the following steady, two-dimensional,...Ch. 9 - Consider the following steady, two-dimensional,...Ch. 9 - Consider liquid in a cylindrical tank. Both the...Ch. 9 - Engine oil at T=60C is forced to flow between two...Ch. 9 - Consider steady, two-dimensional, incompressible...Ch. 9 - Consider steady, incompressible, parallel, laminar...Ch. 9 - Prob. 89PCh. 9 - Prob. 90PCh. 9 - Prob. 91PCh. 9 - The first viscous terms in -comonent of the...Ch. 9 - An incompressible Newtonian liquid is confined...Ch. 9 - Prob. 94PCh. 9 - Prob. 95PCh. 9 - Prob. 96PCh. 9 - Prob. 97PCh. 9 - Consider steady, incompressible, laminar flow of a...Ch. 9 - Consider again the pipe annulus sketched in Fig...Ch. 9 - Repeat Prob. 9-99 except swap the stationary and...Ch. 9 - Consider a modified form of Couette flow in which...Ch. 9 - Consider dimensionless velocity distribution in...Ch. 9 - Consider steady, incompressible, laminar flow of a...Ch. 9 - Prob. 104PCh. 9 - Prob. 105PCh. 9 - Prob. 106PCh. 9 - Prob. 107CPCh. 9 - Prob. 108CPCh. 9 - Discuss the relationship between volumetric strain...Ch. 9 - Prob. 110CPCh. 9 - Prob. 111CPCh. 9 - Prob. 112PCh. 9 - Prob. 113PCh. 9 - Look up the definition of Poisson’s equation in...Ch. 9 - Prob. 115PCh. 9 - Prob. 116PCh. 9 - Prob. 117PCh. 9 - For each of the listed equation, write down the...Ch. 9 - Prob. 119PCh. 9 - Prob. 120PCh. 9 - A block slides down along, straight inclined wall...Ch. 9 - Water flows down a long, straight, inclined pipe...Ch. 9 - Prob. 124PCh. 9 - Prob. 125PCh. 9 - Prob. 126PCh. 9 - Prob. 128PCh. 9 - The Navier-Stokes equation is also known as (a)...Ch. 9 - Which choice is not correct regarding the...Ch. 9 - In thud flow analyses, which boundary condition...Ch. 9 - Which choice is the genera1 differential equation...Ch. 9 - Which choice is the differential , incompressible,...Ch. 9 - A steady, two-dimensional, incompressible flow...Ch. 9 - A steady, two-dimensional, incompressible flow...Ch. 9 - A steady velocity field is given by...Ch. 9 - Prob. 137P
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- Q1:- (a) Show that stream function exists as a consequence ofequation of continuity.(b) Show that potential function exists as a consequence ofirrotational flowarrow_forwardIn the figure, consider the flow on a rotating plate (thick line). Which of the following do we see in the picture? In the picture shown, the radial lines are streamlines coming from the center while the circles are equipotential lines. It is the flow net of a a. b. What is the corresponding stream function for a flow field with velocity potential function, $ = (x² + xy - y²)? C. x² + y² 2 x² + y² y²-x² d. ²+² 2 a. Pathlines b. Streaklines c. Streamlines d. All of the above + 2xy xy a. sink b. vortex c. source d. cannot be determinedarrow_forwardVolumetric strain rate is zero for a steady incompressible flow. In Cartesian coordinates we express this as ∂u/∂x + ∂?/∂y + ∂w/∂z = 0Suppose the characteristic speed and characteristic length for a given flow field are V and L, respectively. Define the following dimensionless variables, Nondimensionalize the equation, and identify any established (named) dimensionless parameters that may appear. Discuss.arrow_forward
- Please don't provide handwritten solution ...arrow_forwardC (C is a constant) 4xy)=xy-2y2+2x2+C (C is a constant) O C. O d. 4(xy)=xy3-2y2+2x2+C (C is a constant) Clear my choice The stream function for a two-dimensional incompressible flow field is y = - 2(x-y), what is the corresponding velocity potential equal? Oa. p = 2(x - y) + C O b. p = 2(x + y) + C p = (x + y) + C O d. p = (x - y) + C Clear my choice Consider a steady two-dimensional, incompressible flow of a Newtonian fluid with the veloc -x and v = y – x, Find the pressure field P(x, y) if the pressure at point O (x= 0, y = field: u = is equal to PO and the velocity field satisfies the Navier-Stokes equations.arrow_forwardSolve it by your hand written form.arrow_forward
- A steady, incompressible, two-dimensional CFD calculation of flow through an asymmetric two-dimensional branching duct reveals the streamline pattern sketched in Fig, where the values of ? are in units of m2/s, and W is the width of the duct into the page. The values of stream function ? on the duct walls are shown. What percentage of the flow goes through the upper branch of the duct?arrow_forwardFor a 2-D irrotation flow, the velocity potential is defined as o = log. (x +y). Which of the following is a possible stream function ự, for this flow? (a) -1 tan -1 (b) tan X (5) 1 (c) 2 tan (d) 2 tan yarrow_forwardWhat is the definition of a timeline? How can timelines be produced in a water channel? Name an application where timelines are more useful than streaklines.arrow_forward
- P1 A thin layer of water flows down a plate inclined to the horizontal with an angle a = 15° in the shown coordinate system. If the thickness of the water layer is a=0.5 mm, assuming that the flow is laminar and incompressible, (water density p = 1000 kg/m³viscosity µ = 0.001 Pa.s and acceleration of gravity g = 9.81 m/s²) and an air flow shears the layer in a direction opposite to its flow with a shear stress of 1 N /m². Solve the Navier-Stokes equation: air water (a) to find the value of the maximum water velocity in m/s to three decimal points, Answer: (b)and to find the value of water velocity at the layer's surface in m/s to three decimal points, Answer:arrow_forwardThe potential function. o., for an incompressible, two-dimensional flow field is given by o=Ux+ Klnr (a) Is this flow possible? (b) Determine the stream function (c) Plot a few streamlines when U = 10m * s ^ - 1 and K = 5m ^ 2 * s ^ - 1 . Note- you will have to work in polar coordinates.arrow_forwardPotential flow against a flat plate (Fig. 1a scribed with the stream function ) can be de- 4 = Axy where A is a constant. This type of flow is commonly called a “stag- nation point" flow since it can be used to describe the flow in the vicinity of the stagnation point at 0. By adding a source of strength m at O, stagnation point flow against a flat plate with a “bump" is ob- tained as illustrated in Fig. 1b ). Determine the relationship be- tween the bump height, h, the constant, A, and the source strength, m. Determine the stream function for streamline passed through stagnation point. Source (a) (b) Figure (1)arrow_forward
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