Verify that the momentum correction factor for fully developed, laminar flow in a circular tube is 4/3.
Read moreTable of Contents
1
Introduction
1.2
Dimensions, Dimensional Homogeneity and Units
1.4
Measures of Fluid Mass and Weight
1.5
Ideal Gas Law
1.6
Viscosity
1.7
Compressibility of Fluids
1.8
Vapor Pressure
1.9
Surface Tension
2
Fluid Statics
2.10
Hydrostatic Force on a Curved Surface
2.11
Buoyancy, Flotation, and Stability
2.12
Pressure Variation in a Fluid with Rigid-Body Motion
2.3
Pressure Variation in a Fluid at Rest
2.4
Standard Atmosphere
2.5
Measurement of Pressure
2.6
Manometry
2.8
Hydrostatic Force on a Plane Surface
3
Elementary Fluid Dynamics- The Bernoulli Equation
3.2
F= ma along a Streamline
3.3
F= ma Normal to a Streamline
3.5
Static, Stagnation, Dynamic, and Total Pressure
3.6
Examples of Use of the Bernoulli Equation
3.6.2
Confined Flows
3.6.3
Flowrate Measurement
3.7
The Energy Line and the Hydraulic Grade Line
3.8
Restrictions on Use of the Bernoulli Equation
4
Fluid Kinematics
4.1
The Velocity Field
4.2
The Acceleration Field
4.2.1
The Material Derivative
4.4
The Reynolds Transport Theorem
5
Finite Control Volume Analysis
5.1
Conservation of Mass- The Continuity Equation
5.1.2
Fixed, Nondeforming Control Volume
Uniform Velocity Profile or Average Velocity
5.1.3
Moving, Nondeforming Control Volume
5.1.4
Deforming Control Volume
5.2
Newton's Second Law- The Linear Momentum and Moment-of-Momentum Equations
5.2.2
Application of the Linear Momentum Equation
(also see Lab Problems 5.1LP, 5.2LP, 5.3LP, and 5.4LP)
5.2.3
Derivation of the Moment-of-Momentum
Equation
5.2.4
Application of the Moment-of-Momentum
Equation
5.3
First Law of Thermodynamics- The Energy Equation
5.3.2
Application of the Energy EquationNo Shaft
Work and Section 5.3.3 The Mechanical Energy Equation
and the Bernoulli Equation
5.3.3
Application of the Energy Equation and the
Bernoulli EquationCombined with Linear Momentum
5.3.4
Application of the Energy Equation to
Nonuniform Flows
5.3.5
Combination of the Energy Equation
and the Moment-of-Momentum Equation
6
Differential Analysis of Fluid Flow
6.1
Fluid Element Kinematics
6.10
Other Aspects of Differential Analysis
6.2
Conservation of Mass
6.3
The Linear Momentum Equation
6.4
Inviscid Flow
6.5
Some Basic, Plane Potential Flows
6.6
Superposition of Basic, Plane Potential Flows
6.8
Viscous Flow
6.9
Some Simple Solutions for Laminar, Viscous, Incompressible Flows
6.9.2
Couette Flow
6.9.3
Steady, Laminar Flow in Circular Tubes
6.9.4
Steady, Axial, Laminar Flow in an Annulus
7
Dimensional Analysis, Similitude, and Modeling
7.1
The Need for Dimensional Analysis
7.10
Similitude Based on Governing Differential Equations
7.3
Determination of Pi Terms
7.5
Determination of Pi Terms by Inspection
7.6
Common Dimensionless Groups in Fluid Mechanics
7.7
Correlation of Experimental Data
7.8
Modeling and Similitude
7.9
Some Typical Model Studies
8
Viscous Flow in Pipes
8.1
General Characteristics of Pipe Flow
8.2
Fully Developed Laminar Flow
8.3
Fully Developed Turbulent Flow
8.4
Dimensional Analysis of Pipe Flow
8.4.2
Minor Losses
8.4.3
Noncircular Conduits
8.5
Pipe Flow Examples
8.5.2
Multiple Pipe Systems
8.6
Pipe Flowrate Measurement
9
Flow Over Immersed Bodies
9.1
General External Flow Characteristics
9.2
Boundary Layer Characteristics
9.3
Drag
9.4
Lift
10
Open-Channel Flow
10.2
Surface Waves
10.3
Energy Considerations
10.4
Uniform Flow
10.4.3
Uniform FlowDetermine Flowrate
10.5
Gradually Varied Flow
10.6
Rapidly Varied Flow
10.6.2, 3
Sharp-Crested and Broad-Crested Weirs
10.6.4
Underflow (Sluice) Gates
11
Compressible Flow
11.1
Ideal Gas Thermodynamics
11.2
Stagnation Properties
11.3
Mach Number and Speed of Sound
11.4
Compressible Flow Regimes
11.5
Shock Waves
11.6
Isentropic Flow
11.7
One-Dimensional Flow in a Variable Area Duct
11.8
Constant-Area Duct Flow With Friction
11.9
Frictionless Flow in a Constant-Area Duct with Heating or Cooling
12
Turbomachines
12.1
Introduction
12.4
The Centrifugal Pump and Section 12.4.1
Theoretical Considerations
12.4.2
Pump Performance Characteristics
12.4.3
Net Positive Suction Head (NPSH)
12.4.4
System Characteristics and Pump Selection
12.5
Dimensionless Parameters and Similarity Laws
12.6
Axial-Flow and Mixed-Flow Pumps
12.7
Fans
12.8
Turbines
12.9
Compressible Flow Turbomachines
Textbook Solutions for Fundamentals of Fluid Mechanics
Chapter 6.9.3 Problem 6.89
Question
A simple flow system to be used for steady-flow tests consistsof a constant head tank connected to a length of 4-mm-diametertubing as shown in Fig. P6.89. The liquid has a viscosity of0.015 N s/m2, a density of 1200 kg/m3, and discharges into theatmosphere with a mean velocity of 2 m/s. (a) Verify that the flowwill be laminar. (b) The flow is fully developed in the last 3 m ofthe tube. What is the pressure at the pressure gage? (c) What is themagnitude of the wall shearing stress, rz, in the fully developedregion?
Solution
The first step in solving 6.9.3 problem number 3 trying to solve the problem we have to refer to the textbook question: A simple flow system to be used for steady-flow tests consistsof a constant head tank connected to a length of 4-mm-diametertubing as shown in Fig. P6.89. The liquid has a viscosity of0.015 N s/m2, a density of 1200 kg/m3, and discharges into theatmosphere with a mean velocity of 2 m/s. (a) Verify that the flowwill be laminar. (b) The flow is fully developed in the last 3 m ofthe tube. What is the pressure at the pressure gage? (c) What is themagnitude of the wall shearing stress, rz, in the fully developedregion?
From the textbook chapter Steady, Laminar Flow in Circular Tubes you will find a few key concepts needed to solve this.
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Title
Fundamentals of Fluid Mechanics 8
Author
Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein
ISBN
9781119080701
A simple flow system to be used for steady-flow tests consistsof a constant head tank
Chapter 6.9.3 textbook questions
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Chapter 6: Problem 6 Fundamentals of Fluid Mechanics 8
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Chapter 6: Problem 6 Fundamentals of Fluid Mechanics 8
Verify that the kinetic energy correction factor for fully developed, laminar flow in a circular tube is 2.0.
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Chapter 6: Problem 6 Fundamentals of Fluid Mechanics 8
A simple flow system to be used for steady-flow tests consists of a constant head tank connected to a length of 4-mm-diameter tubing as shown in Fig. P6.89. The liquid has a viscosity of 0.015 N s/m2 , a density of 1200 kg/m3 , and discharges into the atmosphere with a mean velocity of 2 m/s. (a) Verify that the flow will be laminar. (b) The flow is fully developed in the last 3 m of the tube. What is the pressure at the pressure gage? (c) What is the magnitude of the wall shearing stress, rz, in the fully developed region?
Read more -
Chapter 6: Problem 6 Fundamentals of Fluid Mechanics 8
(a) Show that for Poiseuille flow in a tube of radius R the magnitude of the wall shearing stress, rz, can be obtained from the relationship (rz)wall = 4Q R3 for a Newtonian fluid of viscosity . The volume rate of flow is Q. (b) Determine the magnitude of the wall shearing stress for a fluid having a viscosity of 0.004 N s/m2 flowing with an average velocity of 130 mm/s in a 2-mm-diameter tube.
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Chapter 6: Problem 6 Fundamentals of Fluid Mechanics 8
An infinitely long, solid, vertical cylinder of radius R is located in an infinite mass of an incompressible fluid. Start with the NavierStokes equation in the direction and derive an expression for the velocity distribution for the steady-flow case in which the cylinder is rotating about a fixed axis with a constant angular velocity . You need not consider body forces. Assume that the flow is axisymmetric and the fluid is at rest at infinity.
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Chapter 6: Problem 6 Fundamentals of Fluid Mechanics 8
We will see in Chapter 8 that the pressure drop in fully developed pipe flow is sometimes computed with the aid of a friction factor, defined by f = p 1 2V2 D where V is the average velocity, D is the pipe diameter, and is the length of pipe over which p occurs. For laminar fully developed flow, f can be evaluated from f = C Re where C is a constant and Re is the Reynolds number, given by Re = VD/. Find the constant C for flow in a circular tube.
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Chapter 6: Problem 6 Fundamentals of Fluid Mechanics 8
A liquid (viscosity = 0.002 N s/m2 ; density = 1000 kg/m3 ) is forced through the circular tube shown in Fig. P6.93. A differential manometer is connected to the tube as shown to measure the pressure drop along the tube. When the differential reading, h, is 9 mm, what is the mean velocity in the tube?
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Chapter 6: Problem 6 Fundamentals of Fluid Mechanics 8
Fluid with kinematic viscosity flows down an inclined circular pipe of length and diameter D with flow rate Q. Find the vertical drop per unit length of the pipe so that the pressure drop (p1 p2) is zero for laminar flow.
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Chapter 6: Problem 6 Fundamentals of Fluid Mechanics 8
Blood flows at volume rate Q in a circular tube of radius R. The blood cells concentrate and flow near the center of the tube, while the cell-free fluid (plasma) flows in the outer region. The center core of radius Rc has a viscosity c, and the plasma has a viscosity p. Assume laminar, fully developed flow for both the core and plasma flows and show that an apparent viscosity is defined by app R4 p 8LQ is given by app = p 1 (RcR) 4 (1 p c)
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