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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Chapter 2, Problem 49P
The fluid drive shown transmits a torque T for steady-state conditions (ω1 and ω2 constant). Derive an expression for the slip (ω1 − ω2) in terms of T, μ, d, and h. For values d = 6 in., h = 0.2 in., SAE 30 oil at 75°F, a shaft rotation of 120 rpm, and a torque of 0.003 ft-lbf, determine the slip.
P2.49
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3) The viscosity of the Newtonian fluid with a density of 650 kg/m³
is determined with a viscometer as shown in the figure below. The
required torque (T=F.r) applied to the inner cylinder (r¡ = 4 cm) to
rotate with an angular velocity of 6 rad/s is 3x10-7 Nm. If the
velocity distribution in the clearance between the cylinders is linear,
a) Find the viscosity (µo) of the fluid
b) Find the shear stress on the side surfaces in the viscometer
if the viscosity varies according to µ= H0 (1-r/r2) where r2 =
W=6rad/s
2cm
150mm
ri+2 (cm) due to heating during rotation.
.fluid
A circular step hydrostatic thrust bearing with outside diameter of 16 in. is to be designed to carry a load of 107 700 lbf. The recommended film thickness based on the surface finish is h = 0.003 in. and the lubricant viscosity is μ = 7.85x10-6 reyns. Note that for optimum stiffness ri/ro = 0.53. Take density of the fluid as 880 kg/m3 and cp = 1.88 J/g-Ka) What recess size would you recommend?b) Determine the corresponding pressure and flow rates.c) Determine the pumping power requirement, assuming that pumping efficiencyis 80%.d) Determine the temperature difference between the leakage oil and reservoir.e) Determine the bearing stiffness.
Tutorial Problem #3.
As we discussed in lecture, a concentric cylinder
viscometer is often used to measure the viscosity
(μ) of Newtonian fluids. As shown in the
accompanying figure, the outer cylinder (with
radius Ro) remains stationary while the inner
cylinder (with radius R₁) rotates at an angular
velocity of w (rev/min) and the torque (T) required
to rotate the inner cylinder is measured.
Outer Cylinder
Fluid
Inner Cylinder
T
ω
R₁
R
a. Starting from Newton's law of viscosity, derive the correct equation that is used to calculate u in
μ
terms of w, T, Ro, R₁ and € (the height of the fluid in the gap between the two cylinders). Because
the radial distance between the cylinders (i.e Ro - R₁) is quite small, you can assume that the velocity
profile of the fluid varies linearly with respect to distance between the cylinders.
HINT #1: Torque is the required force multiplied by the moment arm (which is R¡ in this case)
HINT #2: Multiply the angular velocity by the circumference of the…
Chapter 2 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
Ch. 2 - For the velocity fields given below, determine:...Ch. 2 - For the velocity fields given below, determine:...Ch. 2 - A viscous liquid is sheared between two parallel...Ch. 2 - For the velocity field V=Ax2yi+Bxy2j, where A = 2...Ch. 2 - A fluid flow has the following velocity...Ch. 2 - When an incompressible, nonviscous fluid flows...Ch. 2 - For the free vortex flow the velocities are t =...Ch. 2 - For the forced vortex flow the velocities are t =...Ch. 2 - A velocity field is specified as V=axyi+by2j,...Ch. 2 - A velocity field is given by V=ax3i+bxy3j, where a...
Ch. 2 - The velocity for a steady, incompressible flow in...Ch. 2 - The flow field for an atmospheric flow is given by...Ch. 2 - For the velocity field V=AxiAyj,, where A = 2s 1....Ch. 2 - A velocity field in polar coordinates is given...Ch. 2 - The flow of air near the Earths surface is...Ch. 2 - A velocity field is given by V=aytibxj, where a =...Ch. 2 - Air flows downward toward an infinitely wide...Ch. 2 - Consider the flow described by the velocity field...Ch. 2 - Consider the velocity field V = axi + by(1 + ct)...Ch. 2 - Consider the flow field given in Eulerian...Ch. 2 - A velocity field is given by V=axti+byj, where A =...Ch. 2 - Consider the garden hose of Fig. 2.5. Suppose the...Ch. 2 - Consider the velocity field of Problem 2.18. Plot...Ch. 2 - Streaklines are traced out by neutrally buoyant...Ch. 2 - Consider the flow field V=axti+bj, where a = 1/s2...Ch. 2 - A flow is described by velocity field V=ay2i+bj,...Ch. 2 - Tiny hydrogen bubbles are being used as tracers to...Ch. 2 - A flow is described by velocity field V=ai+bxj,...Ch. 2 - A flow is described by velocity field V=ayi+btj,...Ch. 2 - A flow is described by velocity field V=ati+bj,...Ch. 2 - The variation with temperature of the viscosity of...Ch. 2 - The variation with temperature of the viscosity of...Ch. 2 - Some experimental data for the viscosity of helium...Ch. 2 - The velocity distribution for laminar flow between...Ch. 2 - What is the ratio between the viscosities of air...Ch. 2 - Calculate velocity gradients and shear stress for...Ch. 2 - A very large thin plate is centered in a gap of...Ch. 2 - A female freestyle ice skater, weighing 100 lbf,...Ch. 2 - A block of mass 10 kg and measuring 250 mm on each...Ch. 2 - A 73-mm-diameter aluminum (SG = 2.64) piston of...Ch. 2 - A vertical gap 25 mm wide of infinite extent...Ch. 2 - A cylinder 8 in. in diameter and 3 ft long is...Ch. 2 - Crude oil at 20C fills the space between two...Ch. 2 - The piston in Problem 2.40 is traveling at...Ch. 2 - A block of mass M slides on a thin film of oil....Ch. 2 - A block 0.1 m square, with 5 kg mass, slides down...Ch. 2 - A torque of 4 N m is required to rotate the...Ch. 2 - A circular disk of diameter d is slowly rotated in...Ch. 2 - The fluid drive shown transmits a torque T for...Ch. 2 - A block that is a mm square slides across a flat...Ch. 2 - In a food-processing plant, honey is pumped...Ch. 2 - SAE 10W-30 oil at 100C is pumped through a tube L...Ch. 2 - The lubricant has a kinematic viscosity of 2:8105...Ch. 2 - Calculate the approximate viscosity of the oil....Ch. 2 - Calculate the approximate power lost in friction...Ch. 2 - Fluids of viscosities 1 = 0.1 Ns/m2 and 2 = 0.15...Ch. 2 - A concentric cylinder viscometer may be formed by...Ch. 2 - A concentric cylinder viscometer is driven by a...Ch. 2 - A shaft with outside diameter of 18 mm turns at 20...Ch. 2 - A shock-free coupling for a low-power mechanical...Ch. 2 - A proposal has been made to use a pair of parallel...Ch. 2 - The cone and plate viscometer shown is an...Ch. 2 - A viscometer is used to measure the viscosity of a...Ch. 2 - A concentric-cylinder viscometer is shown. Viscous...Ch. 2 - Design a concentric-cylinder viscometer to measure...Ch. 2 - A cross section of a rotating bearing is shown....Ch. 2 - Small gas bubbles form in soda when a bottle or...Ch. 2 - You intend to gently place several steel needles...Ch. 2 - According to Folsom [6], the capillary rise h...Ch. 2 - Calculate and plot the maximum capillary rise of...Ch. 2 - Calculate the maximum capillary rise of water...Ch. 2 - Calculate the maximum capillary depression of...Ch. 2 - Water usually is assumed to be incompressible when...Ch. 2 - The viscous boundary layer velocity profile shown...Ch. 2 - In a food industry process, carbon tetrachloride...Ch. 2 - What is the Reynolds number of water at 20C...Ch. 2 - A supersonic aircraft travels at 2700 km/hr at an...Ch. 2 - SAE 30 oil at 100C flows through a 12-mm-diameter...Ch. 2 - A seaplane is flying at 100 mph through air at...Ch. 2 - An airliner is cruising at an altitude of 5.5 km...
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