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 2, Problem 65P
Design a concentric-cylinder viscometer to measure the viscosity of a liquid similar to water. The goal is to achieve a measurement accuracy of ±1 percent. Specify the configuration and dimensions of the viscometer. Indicate what measured parameter will be used to infer the viscosity of the liquid sample.
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A concentric cylinder viscometer is driven by a falling mass M connected by a cord and pulley to the inner cylinder. Annular gap of width a and height H has been filled with liquid to be tested. The speed of the falling mass is Vm. Develop an algebraic expression for the viscosity of the liquid. Evaluate the viscosity of the liquid using M= 0.1 Kg, R=50mm, H=80 mm, r=25mm, a=0.20mm and Vm = 94
HEATING UNIT
THERMOMETER
LIQUID BATH
Fluid
CONTAINER
CORK
60 CC-
RESERVOIR
Figure 4: Schematic for SAYBOLT viscometer.
a) Explain the operation procedures and constraints of the different viscometers especially
the used one.
b) Explain, with examples, the effects of temperature and shear forces on theNewtonian and
non-Newtonian fluids.
c) Illustrate the results of the viscosity test
of the above motor oil then f it the viscosity
function of temperature to the following logarithmic quadratic correlation as described
below. Find the values for the constants a, b, and c. Takeu at T = 0°C.
То
+ c
T
10
In-
= a + b
Mo
T
d) What is the viscosity of the used
above equation
motor oil at 280 K, 305 K and 3 20 K? You can use the
Part 1: Rotating Viscometer
One type of viscometer involves the use of a rotating cylinder inside a fixed cylinder as shown in
the figure below. The gap between the cylinders must be very small to achieve a linear velocity
distribution in the liquid. Design a viscometer that will be used to measure the viscosity of motor
SAE 30 oil from 0°C to 100°C.
Here you need to determine and report the following parameters:
a. The dimensions of the two cylinders, lengths, thicknesses and diameters.
b. The gap clearance between the surfaces of the cylinders.
c. The rated power of the driving motor.
d. The rotational speed of the shaft.
e. Assumptions, and operational procedure.
Rotating Drum Viscometer
Drive
Motor
Rotating Cylinder
Viscos Liquid Sample
Stationary Cylinder
Figure 3: Schematic for task 3 part 1.
Part 2: Viscosity Correlation
For the above viscometer:
a. Calculate the applied power function of the oil viscosity over the specified range of
temperature. Plot Power function of…
Chapter 2 Solutions
Fox And Mcdonald's Introduction To Fluid Mechanics
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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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- Absolute viscosity of certain fluid is 2.06 centipoise while its kinematic viscosity is т 22 centistoke. Calculate the specific weight if g = 9.75 %3Darrow_forwardHurry up plzarrow_forwardI already calculated the viscosity to be 1.91 but I don't know how to derive the propagation error calculation of viscosity. helparrow_forward
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- Please answer the problems. Show the complete solution.arrow_forwardTutorial 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…arrow_forward• What is the viscosity of the fluid in the viscometer shown below? The length of the viscometer is 60 cm, the outer diameter of the inner cylinder is 12 cm, the gap between the two cylinder is 0.15 cm, number of revolutions per unit time of inner cylinder is 300 rpm, and the torque is measured to be 1.8 N.m. -Stationary cylinder i- 300 rpm Shaft Fluid 0. 106 N s/m? 0.020 N - s/m? 0. 158 N - s/m? 0.013 N - s/m? The density of an object is 2.6 kg /m. What is the specific gravity of this object? Know the density of water at 4 degree C is 1000 kg /m. O26 O 0.0026 O.0026 kg /m O26 kg /marrow_forward
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