Fox and McDonald's Introduction to Fluid Mechanics
9th Edition
ISBN: 9781118912652
Author: Philip J. Pritchard, John W. Mitchell
Publisher: WILEY
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Textbook Question
Chapter 8, Problem 13P
When a horizontal laminar flow occurs between two parallel plates of infinite extent 0.3 m apart, the velocity at the midpoint between the plates is 2.7 m/s. Calculate (a) the flow rate through a cross section 0.9 m wide, (b) the velocity gradient at the surface of the plate, (c) the wall shearing stress if the fluid has viscosity 1.44 P s, and (d) the pressure drop in each 30 m along the flow.
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An oil (viscosity 1 Pa.s, density 800kg/m3) is flowing in an axisymmetric pipe. The flow is fully developed and laminar and the velocity at the centre of the pipe is = 30cm/s. The velocity cross-sectional profile is parabolic as:
u(r) = U0(1- r2/R2)
. Here r is the distance of the point to the pipe centre where the velocity is u(r). . R is radius of pipe (R=4mm).
Calculate:
the shear stress at the pipe wall
the shear stress within the fluid 2 mm from the pipe wall
the Reynold’s number of the flow
The velocity distribution in a fully developed laminar pipe flow is given by where UCL is the velocity at the centerline, and R is the pipe radius. The fluid density is ρ, and its viscosity is µ. (a) Find the average velocity . (b) Write down the Reynolds number Re based on average velocity and pipe diameter. At what approximate value of this Reynolds number would you expect the flow to become turbulent? Why is this value only approximate? (c) Assume that the stress/strain rate relationship for the fluid is Newtonian. Find the wall shear stress τw in terms of µ, R and UCL. Express the local skin friction coeffient Cf in terms of the Reynolds number Re.
Example 1 The velocity profile in laminar flow through a round pipe is expressed as
2U (1-²/r²)
u =
where U is the average velocity, r is the radial distance from the centre line of the pipe,
and ro is the pipe radius. Draw the dimensionless shear stress profile t/to against r/ro,
where to is the wall shear stress. Find the value of to, when fuel oil having an absolute
viscosity μ = 4 x 10-² N/m² flows with an average velocity of 4 m/s in a pipe of
diameter 150 mm.
Chapter 8 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
Ch. 8 - Consider incompressible flow in a circular...Ch. 8 - What is the maximum flow rate of air that may...Ch. 8 - For flow in circular tubes, transition to...Ch. 8 - An incompressible fluid flows between two infinite...Ch. 8 - Oil is confined in a 4-in.-diameter cylinder by a...Ch. 8 - Viscous oil flows steadily between parallel...Ch. 8 - Calculate for the flow in this two-dimensional...Ch. 8 - The velocity profile in a two-dimensional open...Ch. 8 - A large mass is supported by a piston of diameter...Ch. 8 - A hydraulic jack supports a load of 9000 kg. The...
Ch. 8 - The basic component of a pressure gage tester...Ch. 8 - When a horizontal laminar flow occurs between two...Ch. 8 - In a laminar flow of water of 0:007 m3/s between...Ch. 8 - Consider the simple power-law model for a...Ch. 8 - A sealed journal bearing is formed from concentric...Ch. 8 - Using the profile of Problem 8.15, show that the...Ch. 8 - In a laminar flow between parallel plates spaced...Ch. 8 - A fluid of specific gravity 0.90 flows at a...Ch. 8 - Two immiscible fluids are contained between...Ch. 8 - The record-read head for a computer disk-drive...Ch. 8 - Consider steady, incompressible, and fully...Ch. 8 - In a flow of air between parallel plates spaced...Ch. 8 - Consider fully developed flow between parallel...Ch. 8 - Free-surface waves begin to form on a laminar...Ch. 8 - A viscous-shear pump is made from a stationary...Ch. 8 - The efficiency of the viscous-shear pump of Fig....Ch. 8 - An inventor proposes to make a viscous timer by...Ch. 8 - A continuous belt, passing upward through a...Ch. 8 - A wet paint film of uniform thickness, , is...Ch. 8 - Consider first water and then SAE 10W lubricating...Ch. 8 - Using Eq. A.3 in Appendix A for the viscosity of...Ch. 8 - Consider fully developed laminar flow in the...Ch. 8 - Carbon dioxide flows in a 50-mm-diameter pipe at a...Ch. 8 - Consider fully developed laminar flow in a...Ch. 8 - What is the largest diameter of pipeline that may...Ch. 8 - Consider fully developed laminar flow in the...Ch. 8 - Consider fully developed pressure-driven flow in a...Ch. 8 - In the laminar flow of an oil of viscosity 1 Pa_s,...Ch. 8 - In a laminar flow of 0.007 m3/s in a...Ch. 8 - Consider blood flow in an artery. Blood is...Ch. 8 - The classic Poiseuille flow (Eq. 8.12), is for...Ch. 8 - For pressure-driven, steady, fully developed...Ch. 8 - In a laminar flow in a 12-in.-diameter pipe the...Ch. 8 - A fluid of specific gravity 0.90 flows at a...Ch. 8 - In a food industry plant, two immiscible fluids...Ch. 8 - A horizontal pipe carries fluid in fully developed...Ch. 8 - Kerosene is pumped through a smooth tube with...Ch. 8 - In a flow of water in a 0.3-m-diameter pipe, the...Ch. 8 - A liquid drug, with the viscosity and density of...Ch. 8 - Laufer [5] measured the following data for mean...Ch. 8 - Equation 8.23 gives the power-law velocity profile...Ch. 8 - Consider fully developed laminar flow of water...Ch. 8 - Consider fully developed laminar flow in a...Ch. 8 - If the turbulent velocity profile in a pipe 0.6 m...Ch. 8 - Water flows in a horizontal constant-area pipe;...Ch. 8 - For a given volume flow rate and piping system,...Ch. 8 - Consider the pipe flow from the water tower of...Ch. 8 - At the inlet to a constant-diameter section of the...Ch. 8 - When oil (kinematic viscosity 1 104 m2/s,...Ch. 8 - When fluid of specific weight 50 lb/ft3 flows in a...Ch. 8 - If the head lost in 30-m-diameter of...Ch. 8 - Water flows at 10 L/min through a horizontal...Ch. 8 - Laufer [5] measured the following data for mean...Ch. 8 - Water is pumped at the rate of 0.075 m3/s from a...Ch. 8 - Just downstream from the nozzle tip the velocity...Ch. 8 - A horizontal nozzle having a cylindrical tip of 75...Ch. 8 - When 0.3 m3/s of water flows through a...Ch. 8 - Water flows through a 2-in.-diameter tube that...Ch. 8 - A 50-mm-diameter nozzle terminates a vertical...Ch. 8 - A 12-in.-diameter pipe leaves a reservoir of...Ch. 8 - A water pipe gradually changes from 6-in.-diameter...Ch. 8 - Air at standard conditions flows through a sudden...Ch. 8 - Water flows from a larger pipe, diameter D1 = 100...Ch. 8 - Flow through a sudden contraction is shown. The...Ch. 8 - A flow rate of 1.01/min of oil of specific gravity...Ch. 8 - Water flows in a smooth pipeline at a Reynolds...Ch. 8 - Air flows out of a clean room test chamber through...Ch. 8 - A conical diffuser is used to expand a pipe flow...Ch. 8 - By applying the basic equations to a control...Ch. 8 - Water at 45C enters a shower head through a...Ch. 8 - Water discharges to atmosphere from a large...Ch. 8 - A laboratory experiment is set up to measure...Ch. 8 - Oil with kinematic viscosity = 7.5 104 ft2/s...Ch. 8 - Water from a pump flows through a 9-in.-diameter...Ch. 8 - A 5-cm-diameter potable water line is to be run...Ch. 8 - A system for testing variable-output pumps...Ch. 8 - Two reservoirs are connected by three clean...Ch. 8 - Water, at volume flow rate Q = 0.75 ft3/s, is...Ch. 8 - When you drink a beverage with a straw, you need...Ch. 8 - What flow rate (gpm) will be produced in a...Ch. 8 - Gasoline flows in a long, underground pipeline at...Ch. 8 - An 18-in.-diameter new riveted steel pipeline 1000...Ch. 8 - What diameter of smooth masonry pipe is needed to...Ch. 8 - Water flows steadily in a 125-mm-diameter...Ch. 8 - Two galvanized iron pipes of diameter D are...Ch. 8 - A mining engineer plans to do hydraulic mining...Ch. 8 - The flow of water through a 150-mm-diameter...Ch. 8 - The fluid flowing has specific gravity 0.90; V75=6...Ch. 8 - Water is flowing. Calculate the direction and...Ch. 8 - Investigate the effect of tube roughness on flow...Ch. 8 - Investigate the effect of tube length on water...Ch. 8 - For the pipe flow into a reservoir of Example 8.5...Ch. 8 - Calculate the magnitude and direction of the...Ch. 8 - Experimental determination of local losses and...Ch. 8 - Water is flowing. Calculate the gage reading when...Ch. 8 - The siphon shown is fabricated from 50-mm-i.d....Ch. 8 - A large open water tank has a horizontal cast iron...Ch. 8 - A tank containing 30 m3 of kerosene is to be...Ch. 8 - A 90 screwed elbow is installed in a...Ch. 8 - Calculate the total tension in the bolts. Neglect...Ch. 8 - A horizontal 50-mm-diameter PVC pipeline leaves...Ch. 8 - You are watering your lawn with an old hose....Ch. 8 - Your boss claims that for pipe flow the flow rate,...Ch. 8 - A hydraulic press is powered by a remote...Ch. 8 - One-quarter of a cubic meter per second of liquid...Ch. 8 - Calculate the flow rate from this water tank if...Ch. 8 - A 6-ft-diameter pipeline 4 miles long between two...Ch. 8 - A new industrial plant requires a water flow rate...Ch. 8 - What diameter water pipe is required to handle...Ch. 8 - A pipe friction experiment for air consists of a...Ch. 8 - Oil has been flowing from a large tank on a hill...Ch. 8 - The pressure rise across a water pump is 35 psi...Ch. 8 - Cooling water is pumped from a reservoir to rock...Ch. 8 - You are asked to size a pump for installation in...Ch. 8 - Heavy crude oil (SG = 0.925 and = 1.0 104 m2/s)...Ch. 8 - Petroleum products are transported over long...Ch. 8 - The head versus capacity curve for a certain fan...Ch. 8 - A swimming pool has a partial-flow filtration...Ch. 8 - Water at 65C flows through a 75-mm-diameter...Ch. 8 - A 12 in. 6 in. Venturi meter is installed in a...Ch. 8 - A 1-in.-diameter nozzle is attached to a...Ch. 8 - A sharp-edged orifice with conventional pressure...Ch. 8 - A venturi meter with a 3-in.-diameter throat is...Ch. 8 - Air flows through a venturi meter with a...Ch. 8 - Water at 10C flows steadily through a venturi. The...Ch. 8 - Drinking straws are to be used to improve the air...Ch. 8 - In some western states, water for mining and...
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