Solucionario chapra primer capitulo 5ta edicion
1.1 For body weight:
[pic]
TW = 1.5%
For total body water:
[pic]
IW = 55%
1.2
[pic]
[pic]
[pic]
Therefore, the final temperature is 20 + 10.50615 = 30.50615oC.
1.3 This is a transient computation. For the period from ending June 1:
Balance = Previous Balance + Deposits – Withdrawals
Balance =1512.33 + 220.13 – 327.26 = 1405.20
The balances for the remainder of the periods can be computed in a similar fashion as tabulated below:
|Date |Deposit |Withdrawal |Balance |
|1-May | | | $ 1512.33 |
| | $ 220.13 | $ 327.26 | |
|1-Jun | | | $1405.20 |
| | $ 216.80 | $ 378.61 | |
|1-Jul | | | $ 1243.39 |
| | $ 450.25 | $ 106.80 | |
|1-Aug | | | $ 1586.84 |
| | $ 127.31 | $ 350.61 | |
|1-Sep | | |$ 1363.54 |
1.4 [pic]
[pic]
1.5 [pic]
[pic]
[pic]
[pic]
1.6 [pic]
jumper #1: [pic]
jumper #2: [pic]
[pic]
[pic]
[pic]
[pic]
1.7 You are given the following differential equation with the initial condition, v(t = 0) = v(0),
[pic]
The most efficient way to solve this iswith Laplace transforms
[pic]
Solve algebraically for the transformed velocity
[pic] (1)
The second term on the right of the equal sign can be expanded with partial fractions
[pic]
Combining the right-hand side gives
[pic]
By equating like terms in the numerator, the following must hold
[pic]
The firstequation can be solved for A = mg/c. According to the second equation, B = –A. Therefore, the partial fraction expansion is
[pic]
This can be substituted into Eq. 1 to give
[pic]
Taking inverse Laplace transforms yields
[pic]
or collecting terms
[pic]
The first part is the general solution and the second part is the particularsolution for the constant forcing function due to gravity.
1.8 At t = 10 s, the analytical solution is 44.87 (Example 1.1). The relative error can be calculated with
[pic]
The numerical results are:
|step |v(10) |absolute |
| | |relative error |
|2 |47.9690 |6.90% |
|1|46.3639 |3.32% |
|0.5 |45.6044 |1.63% |
The error versus step size can then be plotted as
[pic]
Thus, halving the step size approximately halves the error.
1.9 (a) You are given the following differential equation with the initial condition, v(t = 0) = 0,
[pic]
Multiply both sides by m/c([pic]
Define [pic]
[pic]
Integrate by separation of variables,
[pic]
A table of integrals can be consulted to find that
[pic]
Therefore, the integration yields
[pic]
If v = 0 at t = 0, then because tanh–1(0) = 0, the constant of integration C = 0 and the solution is
[pic]
This result can thenbe rearranged to yield
[pic]
(b) Using Euler’s method, the first two steps can be computed as
[pic]
[pic]
The computation can be continued and the results summarized and plotted as:
|t |v |dv/dt |
|0 |0 |9.8 |
|2 |19.6 |8.53075 |
|4 |36.6615...
Regístrate para leer el documento completo.