EBK NUMERICAL METHODS FOR ENGINEERS
EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 8220100254147
Author: Chapra
Publisher: MCG
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Chapter 24, Problem 40P

The rate of cooling of a body (Fig. P24.40) can be expressed as

d T d t = k ( T T a )

Where T = temperature of the body  ( ° C ) , T a = temperature of  the surrounding medium ( ° C ) , and k = a a proportionality constant (per minute). Thus, this equation (called Newton's law of cooling) specifies that the rate of cooling is proportional to the difference in the temperatures of the body and of the surrounding medium. If a metal ball heated to 80 °C is dropped into water that is held constant at T a = 20 °C , the temperature of the ball changes, as in

Time, min 0 5 10 15 20 25
T , ° C 80 44.5 30.0 24.1 21.7 20.7

Utilize numerical differentiation to determine d T / d t at each value of time. Plot d T / d t versus T T a and employ linear regression to evaluate k.

Chapter 24, Problem 40P, The rate of cooling of a body (Fig. P24.40) can be expressed as dTdt=k(TTa) Where

FIGURE P24.40

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Problem (17): water flowing in an open channel of a rectangular cross-section with width (b) transitions from a mild slope to a steep slope (i.e., from subcritical to supercritical flow) with normal water depths of (y₁) and (y2), respectively. Given the values of y₁ [m], y₂ [m], and b [m], calculate the discharge in the channel (Q) in [Lit/s]. Givens: y1 = 4.112 m y2 = 0.387 m b = 0.942 m Answers: ( 1 ) 1880.186 lit/s ( 2 ) 4042.945 lit/s ( 3 ) 2553.11 lit/s ( 4 ) 3130.448 lit/s
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Chapter 24 Solutions

EBK NUMERICAL METHODS FOR ENGINEERS

Ch. 24 - One of your colleagues has designed a new...Ch. 24 - Video an giography is used to measure blood flow...Ch. 24 - 24.14 Perform the same computation as in Sec....Ch. 24 - Perform the same computation as in Sec. 24.2, but...Ch. 24 - 24.16 As in Sec. 24.2, compute F using the...Ch. 24 - Stream cross-sectional areas (A) are required for...Ch. 24 - 24.18 As described in Prob. 24.17, the...Ch. 24 - 24.21 A transportation engineering study requires...Ch. 24 - 24.22 A wind force distributed against the side of...Ch. 24 - 24.23 Water exerts pressure on the upstream ...Ch. 24 - 24.24 To estimate the size of a new dam, you have...Ch. 24 - The data listed in the following table gives...Ch. 24 - The heat flux q is the quantity of heat flowing...Ch. 24 - 24.27 The horizontal surface area of a lake at a...Ch. 24 - 24.28 Perform the same computation as in Sec....Ch. 24 - 24.29 Repeat Prob. 24.28, but use five...Ch. 24 - Repeat Prob. 24.28, but use Romberg integration to...Ch. 24 - Faradays law characterizes the voltage drop across...Ch. 24 - 24.32 Based on Faraday’s law (Prob. 24.31), use...Ch. 24 - Suppose that the current through a resistor is...Ch. 24 - If a capacitor initially holds no charge, the...Ch. 24 - 24.35 Perform the same computation as in Sec....Ch. 24 - 24.36 Repeat Prob. 24.35, but use (a) Simpson’s ...Ch. 24 - 24.37 Compute work as described in Sec. 24.4, but...Ch. 24 - As was done in Sec. 24.4, determine the work...Ch. 24 - 24.39 The work done on an object is equal to the...Ch. 24 - The rate of cooling of a body (Fig. P24.40) can be...Ch. 24 - 24.41 A rod subject to an axial load (Fig....Ch. 24 - If the velocity distribution of a fluid flowing...Ch. 24 - 24.43 Using the following data, calculate the work...Ch. 24 - 24.44 A jet fighter’s position on an aircraft...Ch. 24 - 24.45 Employ the multiple-application Simpson’s...Ch. 24 - The upward velocity of a rocket can be computed by...Ch. 24 - Referring to the data from Problem 20.61, find the...Ch. 24 - Fully developed flow moving through a 40-cm...Ch. 24 - Fully developed flow of a Bingham plasticfluid...Ch. 24 - 24.50 The enthalpy of a real gas is a ...Ch. 24 - Given the data below, find the isothermal work...Ch. 24 - 24.52 The Rosin-Rammler-Bennet (RRB) equation is...Ch. 24 - For fluid flow over a surface, the heat flux to...Ch. 24 - The pressure gradient for laminar flow through a...Ch. 24 - 24.55 Velocity data for air are collected at...
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