EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Textbook Question
Chapter 20, Problem 58P
Andrade's equation has been proposed as a model of theeffect of temperature on viscosity,
where
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The viscous torque T produced on a disc rotating in a liquid depends upon the
characteristic dimension D, the rotational speed N, the density pand the dynamic
viscosity u.
a) Show that there are two non-dimensional parameters written as:
T
and a,
PND?
b) In order to predict the torque on a disc of 0.5 m of diameter which rotates in oil at
200 rpm, a model is made to a scale of 1/5. The model is rotated in water.
Calculate the speed of rotation of the model necessary to simulate the rotation of
the real disc.
c) When the model is tested at 18.75 rpm, the torque was 0.02 N.m. Predict the
torque on the full size disc at 200 rpm.
Notes: For the oil: the density is 750kg/m² and the dynamic viscosity is 0.2 N.s/m².
For water: the density is 1000 kg/ m² and the dynamic viscosity is 0.001 N.s/m².
kg.m
IN =1
b) The following shear stress – shear rate behavior was observed.
Shear rate (Seconds-1)
Shear Stress (dynes/cm?)
20
11
30
15.2
40
19.1
50
22.9
60
26.5
1.
Make a plot of shear stress (ordinate) vs shear rate (abscissa) on log-log paper.
2.
Can the fluid behavior be accurately modeled by the Newtonian, Bingham plastic,
or Power law model?
A- Womersley number (a) of a human aorta is 20 and for the rabbit aorta is 17, the blood density is approximately the same across the species. The values of viscosity were 0.0035 Ns/m² for the human and 0.0040 Ns/m² for the rabbit. The diameter of the aorta is 2.0 cm for the man, and 0.7 cm for the rabbit, estimate the heart rate beats per minute (bpm) for both species
Chapter 20 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 20 - 20.1 Perform the same computation as in Sec. 20.1,...Ch. 20 - You perform experiments and determine the...Ch. 20 - 20.3 It is known that the tensile strength of a...Ch. 20 - Prob. 4PCh. 20 - 20.5 The specific volume of a superheated steam is...Ch. 20 - Prob. 6PCh. 20 - In Alzheimers disease, the number of neurons in...Ch. 20 - 20.8 The following data were taken from a stirred...Ch. 20 - Prob. 9PCh. 20 - Concentration data were taken at 15 time points...
Ch. 20 - Prob. 11PCh. 20 - The molecular weight of a polymer can be...Ch. 20 - 20.13 On average, the surface area A of human...Ch. 20 - 20.14 Determine an equation to predict metabolism...Ch. 20 - 20.15 Human blood behaves as a Newtonian fluid...Ch. 20 - 20.16 Soft tissue follows an exponential...Ch. 20 - 20.17 The thickness of the retina changes during...Ch. 20 - 20.18 The data tabulated below were generated from...Ch. 20 - The shear stresses, in kilopascals (kPa), of nine...Ch. 20 - 20.20 A transportation engineering study was...Ch. 20 - The saturation concentration of dissolved oxygen...Ch. 20 - For the data in Table P20.21, use polynomial...Ch. 20 - 20.23 Use multiple linear regression to derive a...Ch. 20 - 20.24 As compared to the models from Probs. 20.22...Ch. 20 - 20.25 In water-resources engineering, the sizing...Ch. 20 - 20.26 The concentration of total phosphorus and...Ch. 20 - 20.27 The vertical stress under the corner of a...Ch. 20 - Three disease-carrying organisms decay...Ch. 20 - 20.29 The mast of a sailboat has a cross-sectional...Ch. 20 - 20.30 Enzymatic reactions are used extensively to...Ch. 20 - 20.31 Environmental engineers dealing with the...Ch. 20 - An environmental engineer has reported the data...Ch. 20 - The following model is frequently used in...Ch. 20 - 20.34 As a member of Engineers Without Borders,...Ch. 20 - 20.35 Perform the same computations as in Sec....Ch. 20 - 20.36 You measure the voltage drop V across a...Ch. 20 - Duplicate the computation for Prob. 20.36, but use...Ch. 20 - The current in a wire is measured with great...Ch. 20 - 20.39 The following data was taken from an...Ch. 20 - It is known that the voltage drop across an...Ch. 20 - Ohms law states that the voltage drop V across an...Ch. 20 - 20.42 Repeat Prob. 20.41 but determine the...Ch. 20 - 20.43 An experiment is performed to determine the...Ch. 20 - Bessel functions often arise in advanced...Ch. 20 - 20.45 The population of a small community on the...Ch. 20 - Based on Table 20.4, use linear and quadratic...Ch. 20 - 20.47 Reproduce Sec. 20.4, but develop an equation...Ch. 20 - 20.48 Dynamic viscosity of water is related to...Ch. 20 - 20.49 Hooke’s law, which holds when a spring is...Ch. 20 - 20.50 Repeat Prob. 20.49 but fit a power curve to...Ch. 20 - The distance required to stop an automobile...Ch. 20 - An experiment is performed to define the...Ch. 20 - The acceleration due to gravity at an altitude y...Ch. 20 - The creep rate is the time rate at which strain...Ch. 20 - 20.55 It is a common practice when examining a...Ch. 20 - The relationship between stress and the shear...Ch. 20 - The velocity u of air flowing past a flat surface...Ch. 20 - 20.58 Andrade’s equation has been proposed as a...Ch. 20 - Develop equations to fit the ideal specific heats...Ch. 20 - 20.60 Temperatures are measured at various points...Ch. 20 - 20.61 The data below were obtained from a creep...
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- Table 1 shows the variation of dynamic viscosities of water with absolute temperature. Table 1: Dynamic viscosity of water with absolute temperature. Viscosity µ, Pa.s x 10-³ 1.787 Temperature, K 273.15 278.15 283.15 293.15 303.15 1 313.15 333.15 353.15 373.15 4G 1.519 1.307 1.002 0.7975 0.6529 0.4665 0.3547 0.2828 a) Using excel software, develop a relationship of for viscosity in the form of μ=A+BT+CT² + DT³ + ET. Done Show your trend line regression and standard deviation for linear and polynomial index (quadratic T², cubic T³ and T). b) Using the relationship developed, predict the dynamic viscosity of water at 50 °C at which the reported value is 5.468 x 10 Pa.s. Compare your result with the results of Andrade's equation which is given in the form of μ = D.e BT where D and B are constants whose values are to be determined using viscosity data given.arrow_forwardSaturated steam at 99.6 °C is heated to 350°C. Use the steam table provided to determine: a. The required heat input if 1 kg of steam undergoes the process in a variable-volume constant-pressure container. b. The work of expansion (in kJ) of the steam undergoing the process. C. The required heat input if a continuous stream flowing at 1 kg/s undergoes the process at constant pressure. d. Does your numeric answer to part c equal the sum of parts b and a? Explain why or why not. Given: 1 bar = 10 N/m4, Q= AH, Q = AU, AA = AÛ + PAV, table B.7 in kJ/kg and m/kg.arrow_forwardTorque T needed to rotate a disk in a liquid depends on the diameter D, the angular velocity w, the fluid density p and viscosity, and the distance from the wall x. Relate torque to the other variables using the MLT system. Justify reasons for the chosen repeating variables.arrow_forward
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