Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 10, Problem 56P
To determine
Whether the steam function
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(c) A flow field consists of two free vortices which are rotating in clockwise direction
with the strengths, K of 20 m²/s and 15 m/s located at points A(3, 3) and B(-4,-4)
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Sketch the whole flow field and indicate all the points (A, B, C and stagnation
(i)
point(s), note that point C (-4,0) is given in part (iii)) and velocities involved
clearly.
(ii) Find the stagnation point or points of this flow field and indicate the coordinate
or coordinates clearly.
(iii) Find the resultant velocity (both magnitude and angle with x-axis) at point
C(-4, 0).
K
Note: For free vortex, the velocity components are v, = 0 and v, ==.
r
A unifom flow field defined by y = y is superposed on =xi- vị. Determine the stream
function and velocity potential for the ocombined flow
[Ans. y = xy +y, =
+x-
2
For an incompressible flow on xz-plane, write down the continuity equation. Define an appropriate
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Chapter 10 Solutions
Fluid Mechanics: Fundamentals and Applications
Ch. 10 - Discuss how nondimensalizsionalization of the...Ch. 10 - Prob. 2CPCh. 10 - Expalain the difference between an “exact”...Ch. 10 - Prob. 4CPCh. 10 - Prob. 5CPCh. 10 - Prob. 6CPCh. 10 - Prob. 7CPCh. 10 - A box fan sits on the floor of a very large room...Ch. 10 - Prob. 9PCh. 10 - Prob. 10P
Ch. 10 - Prob. 11PCh. 10 - In Example 9-18 we solved the Navier-Stekes...Ch. 10 - Prob. 13PCh. 10 - A flow field is simulated by a computational fluid...Ch. 10 - In Chap. 9(Example 9-15), we generated an “exact”...Ch. 10 - Prob. 16CPCh. 10 - Prob. 17CPCh. 10 - A person drops 3 aluminum balls of diameters 2 mm,...Ch. 10 - Prob. 19PCh. 10 - Prob. 20PCh. 10 - Prob. 21PCh. 10 - Prob. 22PCh. 10 - Prob. 23PCh. 10 - Prob. 24PCh. 10 - Prob. 25PCh. 10 - Prob. 26PCh. 10 - Prob. 27PCh. 10 - Consider again the slipper-pad bearing of Prob....Ch. 10 - Consider again the slipper the slipper-pad bearing...Ch. 10 - Prob. 30PCh. 10 - Prob. 31PCh. 10 - Prob. 32PCh. 10 - Prob. 33PCh. 10 - Prob. 34EPCh. 10 - Discuss what happens when oil temperature...Ch. 10 - Prob. 36PCh. 10 - Prob. 38PCh. 10 - Prob. 39CPCh. 10 - Prob. 40CPCh. 10 - Prob. 41PCh. 10 - Prob. 42PCh. 10 - Prob. 43PCh. 10 - Prob. 44PCh. 10 - Prob. 45PCh. 10 - Prob. 46PCh. 10 - Prob. 47PCh. 10 - Prob. 48PCh. 10 -
Ch. 10 - Prob. 50CPCh. 10 - Consider the flow field produced by a hair dayer...Ch. 10 - In an irrotational region of flow, the velocity...Ch. 10 -
Ch. 10 - Prob. 54CPCh. 10 - Prob. 55PCh. 10 - Prob. 56PCh. 10 - Consider the following steady, two-dimensional,...Ch. 10 - Prob. 58PCh. 10 - Consider the following steady, two-dimensional,...Ch. 10 - Prob. 60PCh. 10 - Consider a steady, two-dimensional,...Ch. 10 -
Ch. 10 - Prob. 63PCh. 10 - Prob. 64PCh. 10 - Prob. 65PCh. 10 - In an irrotational region of flow, we wtite the...Ch. 10 - Prob. 67PCh. 10 - Prob. 68PCh. 10 - Water at atmospheric pressure and temperature...Ch. 10 - The stream function for steady, incompressible,...Ch. 10 -
Ch. 10 - We usually think of boundary layers as occurring...Ch. 10 - Prob. 73CPCh. 10 - Prob. 74CPCh. 10 - Prob. 75CPCh. 10 - Prob. 76CPCh. 10 - Prob. 77CPCh. 10 - Prob. 78CPCh. 10 - Prob. 79CPCh. 10 - Prob. 80CPCh. 10 - Prob. 81CPCh. 10 -
Ch. 10 - On a hot day (T=30C) , a truck moves along the...Ch. 10 - A boat moves through water (T=40F) .18.0 mi/h. A...Ch. 10 - Air flows parallel to a speed limit sign along the...Ch. 10 - Air flows through the test section of a small wind...Ch. 10 - Prob. 87EPCh. 10 - Consider the Blasius solution for a laminar flat...Ch. 10 - Prob. 89PCh. 10 - A laminar flow wind tunnel has a test is 30cm in...Ch. 10 - Repeat the calculation of Prob. 10-90, except for...Ch. 10 - Prob. 92PCh. 10 - Prob. 93EPCh. 10 - Prob. 94EPCh. 10 - In order to avoid boundary laver interference,...Ch. 10 - The stramwise velocity component of steady,...Ch. 10 - For the linear approximation of Prob. 10-97, use...Ch. 10 - Prob. 99PCh. 10 - One dimension of a rectangular fiat place is twice...Ch. 10 - Prob. 101PCh. 10 - Prob. 102PCh. 10 - Prob. 103PCh. 10 - Static pressure P is measured at two locations...Ch. 10 - Prob. 105PCh. 10 - For each statement, choose whether the statement...Ch. 10 - Prob. 107PCh. 10 - Calculate the nine components of the viscous...Ch. 10 - In this chapter, we discuss the line vortex (Fig....Ch. 10 - Calculate the nine components of the viscous...Ch. 10 - Prob. 111PCh. 10 - The streamwise velocity component of a steady...Ch. 10 - For the sine wave approximation of Prob. 10-112,...Ch. 10 - Prob. 115PCh. 10 - Suppose the vertical pipe of prob. 10-115 is now...Ch. 10 - Which choice is not a scaling parameter used to o...Ch. 10 - Prob. 118PCh. 10 - Which dimensionless parameter does not appear m...Ch. 10 - Prob. 120PCh. 10 - Prob. 121PCh. 10 - Prob. 122PCh. 10 - Prob. 123PCh. 10 - Prob. 124PCh. 10 - Prob. 125PCh. 10 - Prob. 126PCh. 10 - Prob. 127PCh. 10 - Prob. 128PCh. 10 - Prob. 129PCh. 10 - Prob. 130PCh. 10 - Prob. 131PCh. 10 - Prob. 132PCh. 10 - Prob. 133PCh. 10 - Prob. 134PCh. 10 - Prob. 135PCh. 10 - Prob. 136PCh. 10 - Prob. 137PCh. 10 - Prob. 138P
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- 5. The velocity components in spherical coordinates of the axisymmetric uniform flow of a viscous fluid past a sphere are 3a Up - = —/U ( 2 + 2 − ³ª). -U T Ug = U U2 - cos 3a 2r sen 27-3 where U is the velocity of the uniform flow and a is the radius of the sphere. Find the Stokes stream function for this flow. Is it a rotational or irrotational flow?arrow_forwardThe stream function for an incompressible, two-dimensional flow field iswhere a and b are constants. Is this an irrotational flow? Explain.arrow_forwardIn a 2D dimension incompressible flow , if the fluid velocity components are given by u = x-4y , v = -4x then stream function y is given byarrow_forward
- Thevelocity components in thex and y directions are given by u = Ary3 – x²y, v = xy? -÷y*. The value of 1 for a possible flow field involving an incompressible fluid isarrow_forwardConsider a planar irrotational region of flow in the r?-plane. Show that stream function ? satisfies the Laplace equation in cylindrical coordinates.arrow_forwardDoes the velocity potential exist for two dimensional incompressible flow prescribed by u = x-4y; v = -(y+4x)? If so determine its form (@) as well as that of stream function (u).arrow_forward
- A two-dimensional flow field has velocities along the x and y directions given by u = x²t and v = - 2xyt respectively, where t is time. The equation of streamlines is:arrow_forwardAy j. Is this a possible case of incompres- 3.9 A velocity field is given by V= Axyi -- %3D sible flow? If yes, obtain the stream function and find the value of constant A for which the flow rate between the streamlines passing through the points (3, 3) and (3, 4) is 18 units. Axy Ans: V = 12 + C, A 7 2arrow_forwardar r rəe 6- Proof that Streamlines and equipotential lines are orthogonal to each otherarrow_forward
- Q1:- (a) Show that stream function exists as a consequence ofequation of continuity.(b) Show that potential function exists as a consequence ofirrotational flowarrow_forwardA 2-D flow field has velocity components along X-axis and y-axis given by u = x't and v = -2 xyt respectively, here, t is time. The equation of streamline for the given velocity field is : (а) ху — сonstant (с) ху' — сonstant (b) x´y = constant (d) x + y constantarrow_forwardCompute the b Am? when the lower plate Steady skte momentum Flex Ey> momentum Ilex ty Velscity v in the Figure beloo is 0.804n/s s the pasitive X-directan, the Separation Y s o 304mm, md the fluid viscosity N is o7cP Naly) Longe t Final uelociny distribution in teady Flowarrow_forward
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