For oil (SG = 0.86, = 0.025 Ns/m2 ) flow of 0.2 m3 /s through a round pipe with diameter of 500 mm, determine the Reynolds number. Is the flow laminar or turbulent?
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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 8.3 Problem 8.28
Question
As shown in Video V8.10 and Fig. P8.28, the velocityprofile for laminar flow in a pipe is quite different fromthat for turbulent flow. With laminar flow the velocity profileis parabolic; with turbulent flow at Re = 10,000 the velocityprofile can be approximated by the power-law profile shown inthe figure. (a) For laminar flow, determine at what radial locationyou would place a Pitot tube if it is to measure the averagevelocity in the pipe. (b) Repeat part (a) for turbulent flow withRe = 10,000.
Solution
The first step in solving 8.3 problem number 2 trying to solve the problem we have to refer to the textbook question: As shown in Video V8.10 and Fig. P8.28, the velocityprofile for laminar flow in a pipe is quite different fromthat for turbulent flow. With laminar flow the velocity profileis parabolic; with turbulent flow at Re = 10,000 the velocityprofile can be approximated by the power-law profile shown inthe figure. (a) For laminar flow, determine at what radial locationyou would place a Pitot tube if it is to measure the averagevelocity in the pipe. (b) Repeat part (a) for turbulent flow withRe = 10,000.
From the textbook chapter Fully Developed Turbulent Flow 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
As shown in Video V8.10 and Fig. P8.28, the velocityprofile for laminar flow in a pipe
Chapter 8.3 textbook questions
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Chapter 8: Problem 8 Fundamentals of Fluid Mechanics 8
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Chapter 8: Problem 8 Fundamentals of Fluid Mechanics 8
As shown in Video V8.10 and Fig. P8.28, the velocity profile for laminar flow in a pipe is quite different from that for turbulent flow. With laminar flow the velocity profile is parabolic; with turbulent flow at Re = 10,000 the velocity profile can be approximated by the power-law profile shown in the figure. (a) For laminar flow, determine at what radial location you would place a Pitot tube if it is to measure the average velocity in the pipe. (b) Repeat part (a) for turbulent flow with Re = 10,000.
Read more -
Chapter 8: Problem 8 Fundamentals of Fluid Mechanics 8
Water at 10 C flows through a smooth 60-mm-diameter pipe with an average velocity of 8 m/s. Would a layer of rust of height 0.005 mm on the pipe wall protrude through the viscous sublayer? Justify your answer with appropriate calculations.
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Chapter 8: Problem 8 Fundamentals of Fluid Mechanics 8
When soup is stirred in a bowl, there is considerable turbulence in the resulting motion (see Video V8.7). From a very simplistic standpoint, this turbulence consists of numerous intertwined swirls, each involving a characteristic diameter and velocity. As time goes by, the smaller swirls (the fine scale structure) die out relatively quickly, leaving the large swirls that continue for quite some time. Explain why this is to be expected.
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Chapter 8: Problem 8 Fundamentals of Fluid Mechanics 8
Water at 60 F flows through a 6-in.-diameter pipe with an average velocity of 15 ft/s. Approximately what is the height of the largest roughness element allowed if this pipe is to be classified as smooth?
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