Theory and Design for Mechanical Measurements
6th Edition
ISBN: 9781118881279
Author: Richard S. Figliola, Donald E. Beasley
Publisher: WILEY
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Chapter 2, Problem 2.35P
Consider the upward flow of water and air in a tube having a circular cross section, as shown in Figure 2.27. If the water and air flow rates are within a certain range, there are slugs of liquid and large gas bubbles flowing upward together. This type of flow is called “slug flow.” The data file gas_ liquidjdata. txt provided in the online supplements contains measurements of pressure made at the wall of a tube in which air and water were flowing. The data were acquired at a sample frequency of 300 Hz. The average flow velocity of the air and water is 1 m/s.
- Construct an amplitude spectrum from the data, and determine the dominant frequency.
- Using the frequency information from part (a), determine the length L shown in the drawing in Figure 2.27. Assume that the dominant frequency is associated with the passage of the bubbles and slugs across the pressure sensor.
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Figure 2.27 Upward gas-liquid flow: slug flow regime. (Photo courtesy of Donald Beasley.)
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Q. As a means of measuring the viscosity, a liquid is forced to flow through two very large parallel plates by applying a pressure gradient, dp/dx. You can assume that the velocity between the plates is given by (Figure1).
Where μ is the fluid viscosity, dp/dx is the pressure gradient and h is the gap between the plates.
a) Derive an expression for the shear stress acting on the top plate, τW.
b) Q' is the flow rate per unit width (i.e. has units of m2/s). Express Q' in terms of τW.
c) When the flow rate per unit width is Q' = 1.2 x 10-4 m2/s, the gap between the plates is 5 mm, the device estimates the shear stress at the top wall to be -0.05 Pa. Estimate the viscosity of the fluid.
Consider the following samples of gases at the same temperature.
REFER IMAGE
Arrange each of these samples in order from lowest to highest:a. pressureb. average kinetic energyc. densityd. root mean square velocityNote: Some samples of gases may have equal values for these attributes. Assume the larger containers have a volume twice the volume of the smaller containers, and assume the mass of an argon atom is twice the mass of a neon atom.
the black sqaure is delta (change) in pressure
Assume that p is a function of average velocity V, pipe length L and diameter D, the pipe roughness e (mean height of roughness of the pipe wall, e.g. in microns), and the fluid density .
1.How many nondimensional parameters are needed to define the nondimensional pressure-drop vs. flow relationship in the pipe?
2. Using (D, , and V) as repeating parameters, derive the nondimensional pressure drop and other required parameters to relate p, V, L, D, e , and .
Chapter 2 Solutions
Theory and Design for Mechanical Measurements
Ch. 2 - Prob. 2.1PCh. 2 - Prob. 2.2PCh. 2 - Research and describe the importance of...Ch. 2 - Research and describe the importance of data...Ch. 2 - Determine the average and rms values for the func...Ch. 2 - Prob. 2.6PCh. 2 - Prob. 2.9PCh. 2 - Prob. 2.10PCh. 2 - Prob. 2.11PCh. 2 - Prob. 2.12P
Ch. 2 - Express the function y(t) = 4 sin 2xt + 15 cos...Ch. 2 - Prob. 2.14PCh. 2 - The Fourier series that formed the result for...Ch. 2 - The nth partial sum of a Fourier series is defined...Ch. 2 - For the Fourier series given by where t is time in...Ch. 2 - Determine the Fourier series for the function y(t)...Ch. 2 - Show that y(t) = f2(—jc < t < k), y(t + 2k) = y(t)...Ch. 2 - Find the Fourier series of the function shown in...Ch. 2 - Determine the Fourier series for the function y(t)...Ch. 2 - Determine the Fourier series that represents the...Ch. 2 - Consider the triangle wave shown in Figure 2.26 as...Ch. 2 - Prob. 2.24PCh. 2 - A particle executes linear harmonic motion around...Ch. 2 - Define the following characteristics of signals:...Ch. 2 - Construct an amplitude spectrum plot for the...Ch. 2 - Prob. 2.28PCh. 2 - Sketch representative waveforms of the following...Ch. 2 - Represent the function e(t) = 5 sin 31 At + 2 sin...Ch. 2 - Repeat Problem 2.30 using a data set of 256 num...Ch. 2 - A particular strain sensor is mounted to an...Ch. 2 - Prob. 2.33PCh. 2 - Prob. 2.34PCh. 2 - Consider the upward flow of water and air in a...Ch. 2 - Prob. 2.37PCh. 2 - Prob. 2.38PCh. 2 - For the even-functioned triangle wave signal...Ch. 2 - Prob. 2.40P
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