EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Chapter 23, Problem 28P
The velocity profile of a fluid in a circular pipe can be represented as
where
(a) Romberg
(b) Two-point Gauss-Legendre formula, and
(c) The MATLAB quad function. Note that flow is equal to velocity times area.
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A 100 mm by 50 mm Venturi meter is installed in a 100 mm diameter pipe to measure the flow of a certain liquid (sp gr 1.20). A differential gage connected with the inlet and throat contains a substance (sp gr 1.5) in the lower part of the tube, the remainder of the tube being filled with the certain liquid. The difference in height of substance columns in the two legs of the tube is 75 cm. If the coefficient of the meter is 0.97, compute the actual discharge.
(b) A pitot-static probe is use to determine the flow velocity by measuring the differential
pressure. The pitot formula to obtain the flow velocity is,
2(P- P,)
V =
where, V is the velocity, P is pressure and pis fluid density.
i)
The pressure difference sensor use in the system is electronic types and the output
of the device is measured in voltage. The output of the pressure device is 3.5 V and
the linear relationship between the device and the pressure difference is 10 kPa/V.
If the measured fluid is water at 20°C, determine the pressure difference inside the
system the water velocity.
ii)
The Pitot-static tube is also commonly use in aircraft. An aircraft flying at 3000 m
above sea level when the differential pressure reading clocked 3 kPa. Determine the
speed of the aircraft.
Chapter 23 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 23 - 23.1 Compute forward and backward difference...Ch. 23 - 23.2 Repeat Prob. 23.1, but for evaluated at...Ch. 23 - 23.3 Use centered difference approximations to...Ch. 23 - Use Richardson extrapolation to estimate the first...Ch. 23 - Repeat Prob. 23.4, but for the first derivative of...Ch. 23 - 23.6 Employ Eq. (23.9) to determine the first...Ch. 23 - 23.7 Prove that for equispaced data points, Eq....Ch. 23 - Compute the first-order central difference...Ch. 23 - Prob. 9PCh. 23 - Develop a user-friendly program to apply a Romberg...
Ch. 23 - 23.11 Develop a user-friendly program to obtain...Ch. 23 - 23.12 The following data are provided for the...Ch. 23 - 23.13 Recall that for the falling parachutist...Ch. 23 - The normal distribution is defined as f(x)=12ex2/2...Ch. 23 - 23.15 The following data were generated from the...Ch. 23 - Evaluate f/x,f/y, and f/(xy) for the following...Ch. 23 - 23.17 Evaluate the following integral with...Ch. 23 - 23.18 Use the diff command in MATLAB and compute...Ch. 23 - The objective of this problem is to compare...Ch. 23 - Use a Taylor series expansion to derive a centered...Ch. 23 - Use the following data to find the velocity and...Ch. 23 - 23.22 A plane is being tracked by radar, and data...Ch. 23 - 23.23 Develop an Excel VBA macro program to read...Ch. 23 - Use regression to estimate the acceleration at...Ch. 23 - You have to measure the flow rate of water through...Ch. 23 - The velocity y (m/s) of air fl owing past a flat...Ch. 23 - Chemical reactions often follow the model:...Ch. 23 - 23.28 The velocity profile of a fluid in a...Ch. 23 - 23.29 The amount of mass transported via a pipe...
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