Concept explainers
Perform the same computation as in Sec. 32.1, but use

To calculate: The concentration of the distributed-parameter system equations for
Answer to Problem 1P
Solution: The concentration of equations for
Explanation of Solution
Given Information:
The distributed-parameter system depicts chemical modelling being subjected to first order decay and the tank is mixed well vertically and laterally.
Apply finite length of segment,
Here,
is the volume,
is the flow rate,
is the concentration,
is the dispersion coefficient,
is the tank’s cross-sectional area, and
is the first order decay coefficient.
Calculation:
Substitute centred finite differences for the first and the second derivatives in equation (1) to develop steady-state solution,
Further simplify the equation,
And,
Also,
Solve the equation (2),
Substitute
Hence, the required first equation is
Solve the equation (3),
Substitute
Hence, the required middle equation is
Substitute
in middle equation,
Substitute
Substitute
Substitute
Substitute
in middle equation,
Substitute
in middle equation,
Substitute
in middle equation,
Substitute
in middle equation,
Solve equation (4) for last equation,
Substitute
Hence, the required last equation is
Write all the equations in matrix form,
Express the matrix in tri-diagonal form,
Use MATLAB to solve the above matrix.
The output of the program is given below.
Want to see more full solutions like this?
Chapter 32 Solutions
Numerical Methods For Engineers, 7 Ed
- 4.5 Use zero- through third-order Taylor series expansions to predict f(2.5) for f(x) = 25x³- 6x²+7x - 88 using a base point at x = 1. Compute the true percent relative error ε, for each approximation.arrow_forward4.3 Perform the same computation as in Prob. 4.2, but use the Maclaurin series expansion for sin x to estimate sin(л/6). sin x=x- 3x15 3! 5! 7! +arrow_forwardlim 1 x→0x3 L 0 X ln(1+t) dt t4 +4arrow_forward
- Not use ai pleasearrow_forwardA 315-N force F and 70-N-m couple M are applied to co rner A of the block shown. Replace the given force -couple system with an equivalent force -couple systemat corner Darrow_forwardA force and couple are applied to a beam as shown below . (a) Replace this systemwith a single force F applied at point G, and determine the distance d. (b) Solve part aassuming that the directions of the two 600 -N forces are reversed Help finding the distancesarrow_forward
- x If f(x) = = L* f(t)dt then find the value of ƒ (ln 7). f: R R is continuous everywhere.arrow_forwardAn eccentric, compressive 270-lb force P is applied to the end of a cantilever beam. Replace P with an equivalent force-couple system at G.arrow_forwardA 20 lb horizontal force P acts on a bell crank as shown below. (a) Replace P with an equivalent force-couple system at B. (b) Find the two vertical forces at C and D which are equivalent to the couple found in part aarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
