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 5, Problem 14P
Consider a water stream from a jet of an oscillating lawn sprinkler. Describe the corresponding pathline and streakline.
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7. For the flow of a thin layer of liquid down an inclined plane
shown:
a. Using the cross-hatched element and through a force balance,
show
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the
velocity
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dx
y sin e
(b2 - s2)
2 u
Free
Surface
b. Derive an expression for the
liquid velocity at the free
surface.
t dx
Fixed
ys dx
c. Derive an expression for the
discharge per unit width.
d. Derive an expression for the
shear stress at the fixed wall.
Wall
Calculate the discharge passing through a 2-D steady, irrotational and incompressible flow between points (1,3) and (5,4), if stream function is given by ψ = 2x^2y.
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Chapter 5 Solutions
Fox And Mcdonald's Introduction To Fluid Mechanics
Ch. 5 - Which of the following sets of equations represent...Ch. 5 - Which of the following sets of equations represent...Ch. 5 - In an incompressible three-dimensional flow field,...Ch. 5 - In a two-dimensional incompressible flow field,...Ch. 5 - The three components of velocity in a velocity...Ch. 5 - The x component of velocity in a steady,...Ch. 5 - The y component of velocity in a steady...Ch. 5 - The velocity components for an incompressible...Ch. 5 - The radial component of velocity in an...Ch. 5 - A crude approximation for the x component of...
Ch. 5 - A useful approximation for the x component of...Ch. 5 - A useful approximation for the x component of...Ch. 5 - For a flow in the xy plane, the x component of...Ch. 5 - Consider a water stream from a jet of an...Ch. 5 - Which of the following sets of equations represent...Ch. 5 - For an incompressible flow in the r plane, the r...Ch. 5 - A viscous liquid is sheared between two parallel...Ch. 5 - A velocity field in cylindrical coordinates is...Ch. 5 - Determine the family of stream functions that...Ch. 5 - The stream function for a certain incompressible...Ch. 5 - Determine the stream functions for the following...Ch. 5 - Determine the stream function for the steady...Ch. 5 - Prob. 23PCh. 5 - A parabolic velocity profile was used to model...Ch. 5 - A flow field is characterized by the stream...Ch. 5 - A flow field is characterized by the stream...Ch. 5 - Prob. 27PCh. 5 - A flow field is characterized by the stream...Ch. 5 - In a parallel one-dimensional flow in the positive...Ch. 5 - Consider the flow field given by V=xy2i13y3j+xyk....Ch. 5 - Prob. 31PCh. 5 - The velocity field within a laminar boundary layer...Ch. 5 - A velocity field is given by V=10ti10t3j. Show...Ch. 5 - The y component of velocity in a two-dimensional,...Ch. 5 - A 4 m diameter tank is filled with water and then...Ch. 5 - An incompressible liquid with negligible viscosity...Ch. 5 - Sketch the following flow fields and derive...Ch. 5 - Consider the low-speed flow of air between...Ch. 5 - As part of a pollution study, a model...Ch. 5 - As an aircraft flies through a cold front, an...Ch. 5 - Wave flow of an incompressible fluid into a solid...Ch. 5 - A steady, two-dimensional velocity field is given...Ch. 5 - A velocity field is represented by the expression...Ch. 5 - A parabolic approximate velocity profile was used...Ch. 5 - A cubic approximate velocity profile was used in...Ch. 5 - The velocity field for steady inviscid flow from...Ch. 5 - Consider the incompressible flow of a fluid...Ch. 5 - Consider the one-dimensional, incompressible flow...Ch. 5 - Expand (V)V in cylindrical coordinates by direct...Ch. 5 - Determine the velocity potential for (a) a flow...Ch. 5 - Determine whether the following flow fields are...Ch. 5 - The velocity profile for steady flow between...Ch. 5 - Consider the velocity field for flow in a...Ch. 5 - Consider the two-dimensional flow field in which u...Ch. 5 - Consider a flow field represented by the stream...Ch. 5 - Fluid passes through the set of thin, closely...Ch. 5 - A two-dimensional flow field is characterized as u...Ch. 5 - A flow field is represented by the stream function...Ch. 5 - Consider the flow field represented by the stream...Ch. 5 - Consider the flow field represented by the stream...Ch. 5 - Consider the velocity field given by V=Ax2i+Bxyj,...Ch. 5 - Consider again the viscometric flow of Example...Ch. 5 - The velocity field near the core of a tornado can...Ch. 5 - A velocity field is given by V=2i4xjm/s. Determine...Ch. 5 - Consider the pressure-driven flow between...Ch. 5 - Consider a steady, laminar, fully developed,...Ch. 5 - Assume the liquid film in Example 5.9 is not...Ch. 5 - Consider a steady, laminar, fully developed...Ch. 5 - Consider a steady, laminar, fully developed...Ch. 5 - A linear velocity profile was used to model flow...Ch. 5 - A cylinder of radius ri rotates at a speed ...Ch. 5 - The velocity profile for fully developed laminar...Ch. 5 - Assume the liquid film in Example 5.9 is...Ch. 5 - The common thermal polymerase chain reaction (PCR)...Ch. 5 - A tank contains water (20C) at an initial depth y0...Ch. 5 - For a small spherical particle of styrofoam...Ch. 5 - Use Excel to generate the progression to an...
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- Water flows through a garden hose (ID = 20 mm) with a mean velocity of 1.8 m/s. Find the pressure drop for a section of hose that is 30 meters long and situated horizontally. Assume that f = 0.014.arrow_forward7. For the flow of a thin layer of liquid down an inclined plane shown: a. Using the cross-hatched element and through a force balance, show that the velocity distribution across the layer is: dx Y sin e (b2 – s2) 2 µ и 3 Free Surface an expression for the at the free b. Derive t dx liquid velocity surface. c. Derive an discharge per unit width. d. Derive Fixed y s dx expression for the Wall b an expression for the shear stress at the fixed wall.arrow_forward46. Consider the case of an ideal fluid flow in the conduit of Problem 19. Findpressure at the exit of the conduit in terms of the flow density and velocities at theinlet and the outlet.arrow_forward
- Consider a column of water as it falls from a faucet. The opening in the faucet has radius ro and the water comes out with initial velocity vo. Define y to be the distance below the faucet. As the water falls (y increases), it accelerates due to gravity and the stream narrows. a) Assuming streamline flow, find an expression for the velocity of the water for any distance below the faucet. b) The stream obeys the continuity equation. Use this to determine the radius of the stream as a function of y. c) At what distance ₁/2 will the radius of the stream be half its original radius? At what distance Y1/3 will it be a third? d) Compare 1/2 and Y1/3 for v0 = = 1 m/s and v0 = 0.1 m/s (use g = 10 m/s²).arrow_forwardPlease find the question attached.arrow_forwardQ2) Find the value and direction of the force applied on an curved blade as shown in the figure below If the angle(0 = 120°), jet velocity is (30 m/sec), and the 20 discharge 10 L/sec. U2 @=128 U₁ X₂ Farrow_forward
- 1. The water flows through a pipeline 1.2m diameter at a velocity of 3m/swhich bifurcates at a Y-junction into two branches. The first branch is 0.8min diameter and carries 1/3 of the flow, whereas the second branch carriesthe water in a velocity of 2.4m/s. Calculate the following: (i) discharge (ii) velocity in the first branch (iii) diameter of the second brancharrow_forwardA two-dimensional reducing bend has a linear velocity profile at section (1). The flow is uniform at sections (2) and (3). The depth of the bend perpendicular to the plane of the paper is 1 ft. Consider steady incompressible flow. Calculate the discharge at section (1). Also calculate the magnitude and h₁ = 2 ft direction of the uniform velocity at section (3). Hint: the cross-sectional areas are rectangular VA V₁, max 10 ft/s h3 = 1.5 ft- V2 = 15 ft/s - h₂ = 1 ft 0 = 60°arrow_forward3. Theoretical Analysis: [With reference to the Bernoulli and Continuity equations, provide a theoretical analysis of how flowrate can be calculated for a level venturi tube. Label each equation in the theoretical analysis with a number. Explain the steps as per the start given below...] As applied to a pipeline, Bernoulli's equation can be stated as follows: P2 -++ Z1 P1 v? +Z2 (1) Pg 2g Pg 2g I. where the subscripts refer to stations 1 &2 respectively. In this case the elevation head is the same for both stations since the venturi tube is horizontal therefore the Z terms in the above equation can be omitted, giving: 二arrow_forward
- Help with barrow_forwardA 600mm diameter pipeline (A) conveying water splits into two smaller pipelines (B) and (C), 375mm and 225mm respectively in diameter. If the velocity of flow in (A) is 2.0m/sec and the flowrate in (B) is twice that in (C), calculate the flowrate in all pipes and the velocity of flow in pipes (B) and (C)..arrow_forwardIf 475mm diameter pipeline (A) conveying water splits into 2 smaller pipelines (B) and (C), 275mm and 200mm respectively in diameter. If the velocity of flow in (A) is 2.8 m/sec and the flowrate in (B) is twice that in (C), calculate the flowrate in all pipes and the velocity of flow in pipes (B) and (C).arrow_forward
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