A storage tank contains a liquid at depth y where y = 0 when the tank is half full. Liquid is withdrawn at a constant flow rate Q to meet demands. The contents are resupplied at a sinusoidal rate 3Q sin (). Equation can be written for this system as d(Ay) = 3Qsin (1) – d(t) Q (change in = (inflow) – (outflow) volume since the surface area A is constant sin²(t) A dy d(t) Use Euler's method to solve for the depth y from t = 0 to 10 d with a step size of 0.5 d. The parameter values are A = 1200 m² and Q = 500 m³/d. Assume that the initial condition is y = 0.

A storage tank contains a liquid at depth y where y = 0 when the tank is half full. Liquid is withdrawn at a constant flow rate Q to meet demands. The contents are resupplied at a sinusoidal rate 3Q sin (). Equation can be written for this system as d(Ay) = 3Qsin (1) – d(t) Q (change in = (inflow) – (outflow) volume since the surface area A is constant sin²(t) A dy d(t) Use Euler's method to solve for the depth y from t = 0 to 10 d with a step size of 0.5 d. The parameter values are A = 1200 m² and Q = 500 m³/d. Assume that the initial condition is y = 0.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Determine the following: 15.1 transpose of D 15.2 the trace of matrix D

Q: Let R be the triangle with vertices (0,0), (1,2), and (3,0). Find the average value of the function ...

Q: Consider the initial value problem y" - 2y' – 8y = 0, y(0) = a, y'(0) = 3 Find the value of a so tha...

A: Given differential equation is y'' - 2y' - 8y = 0 with y(0) = α , y'(0) = 3

Q: y" +y = 3 et/2) y(0) = 4 y(0) = 3

A: Second order non Homogeneous differential equation

Q: 20. Prove that an angle of 0 radians is constructible if and only if the real number cose(sine) cons...

A: Since θ is constructible, by definition, (cosθ, sinθ) is a constructible point.

Q: Draw a graph of a function that satisfies the following p 1) f(x) 0 for x>0 3) f(0) = 0 %3D 4) f is ...

A: Given description of function 1) f(x)<0 for x<0 2) f(x)>0 for x>0 3) f(0)=0 4) f is alwa...

Q: dx -= In(F (x))+C. What is F (/3) if C=0? For (x+x³) (xtan-'(x) + 1)

Q: Find the determinant of the n×n matrix A with 7's on the diagonal, 1's above the diagonal, and 0's b...

A: Let us consider the given matrix as:A=711111071111007111............000..7n×nThis is an upper diagon...

Q: Exercise 9.2.24. Find matrix inverses in Z26 for the following matrices. If no inverse exists, then ...

Q: Lauren would like to have $55,000 saved 10 years from now. If she finds an account that offers a 3.2...

A: Let the initial investment be P. The compound interest formula for quarterly is A=P1+r44twhere A=tot...

Q: Determine the missing number in the sequence. 2, 5, 8, -- 14, 17

Q: 2.) Calculate the curve integral over the vector field V (xr, y)

A: The curve integrals in the form ∮CVxdx+Vydy involve the integration over a specific path C. In this ...

Q: In Exercises 20-22, construct tables for arithmetic modulo modulo 6 to represent the congruence clas...

A: 22. We have to construct a table for the multiplication modulo 6.That is a table consisting of rema...

Q: 8. Let (X, d) be a metric space, and A, B are subset of X, then (i) Fr(A) = A n (A)° = A – int A (ii...

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for you...

Q: 1-cos 3t 1. Evaluate lim by constructing table of values. 3t t -1 -0.5 -0.01 -0.001 f(t) 1 0.5 0.01 ...

Q: How tall in cm is the stack of 8 cups ?

A: Given- The figure To find- How tall, in cm, is the stack of 8 cups?

Q: LTE 8:01 AM Ø VOLTE il: 4 17% *32. Recall, from Problem 14, that j 2 0 if f(x) > 0 for all x in [a, ...

Q: Let n be a positive integer, and consider the recursive sequence ao = 1, a1 = 1 and for n > 1, An+1 ...

Q: 7. Which of the following is a loop? E F Figure 1 A) BC B) DC C) AE D) None of the above

A: Loop is a closed path, so the from given options only two pints are given so no loop is formed with ...

Q: 3. 1-п

Q: dr For Tatx')(xtan-"(x) + 1) -=In(F(x)) +C. What is F(/3) if C=0? A B -15 -15

Q: 4. Solve the linear system using Cramer's Rule 2y + 5z- 3w = 16 2x + 3y + 32 + 4w = 110 2x + 5y-3z +...

Q: 6. Find the general solution to the differential equation x²y" – 3xy' + 13y = 4 + 3.x (where y' = ) ...

A: To find- Find the general solution to the differential equation x2y'' - 3xy' + 13y = 4 + 3x where y'...

Q: dx = In[F(x)]+C-What is F(/3) if C = For I (x+x*) (x Tan-'x +1) S- SE SI- S-

Q: Compute the Taylor polynomial T5(x) and use the Error Bound to find the maximum possible size of the...

A: Given: f(x)=cos(x), a=0, x=0.175 To find: The Taylor polynomial T5(x) and use the Error Bound to fin...

Q: IJJ is bou bounded and integrable on [a, b] Such that | f(x) | 0).

Q: 7. Which of the following is a loop? A B F Figure 1 A) ВС B) DC C) AE D) None of the above

Q: The percentage of a certain country's national income generated by nonfarm proprietors may be modele...

A: The complete solutions are given below

Q: Show that if a is an even integer, then a =0 (mod 4), and if a is an odd integer, then a =1 (mod 4).

Q: In Exercises 21-26, determine A, X, and B if the system is written as AX = R 22. -3x1-8x2 + 4x3 = -2...

A: The given system is 6x1+4x2-3x3=-7-5x1+3x2+2x3=4

Q: 20. Prove that an angle of e radians is constructible number cos0(sine) if and only if the real cons...

A: Since θ is constructible, by definition, (cosθ, sinθ) is a constructible point.

Q: x+2y =bx + cy

Q: Given the information below, estimate the total distance travelled during these 6 seconds using a le...

A: Introduction: A definite integration of a single variable can be approximated using three different ...

Q: Suppose R is a commutative ring with 1R# 0R. Show that if f (x) = ao + a1a + a2a ++a,n" is a unit in...

Q: L2 0001-(3 1- (p 32 1001 (3 8 001- (a Lて a) 22 6. Find the least nonnegative residue modulo 13 of ea...

A: We find the least nonnegative residue modulo 13 of each of the given integers.

Q: dx +4x = 2e 3 , x(0)= 5 dt (d) dx +4x = sin 2t , x(0)= 0 dt (e)

A: Laplace transferom, solve the differential equation by using Laplace transferom

Q: Problem 3. Factorize 510 + 330i into Gaussian primes. Factorize it in such a way that all the primes...

A: First we have to know about Gaussian prime. Gaussian Prime: A Gaussian integer a+bi where a,b are in...

Q: Determine if this graph is - Planer - Connected - Simple

Q: The antiderivative of f(x), denoted by FX), exhibits an odd symmetry i.e., it satisfies the property...

Q: Fill in the blank: The dual of a linear programming problem have a finite optimal solution, then the...

A: Linear programming:

Q: 1 n > 3. Let an = nVlnn (a) Show that the sequence {an}3 is decreasing. (b) Without computing any li...

Q: - sec?x)emG/e sec³x dr e In (a le) What should be the value of A for to be integrable using the form...

Q: Find the solution to the following initial value problem by finding the general solution to the diff...

Q: 1 Consider the series >) 2 n(1+ ln? n) n=1

Q: 1. Use the Monotone Convergence Theorem to show that the sequence {an} converges, where an = 1- п! f...

Q: Question 3 Solve for x: 32+104 x(mod5) 04 O 2 MAR 21 MacBook Air

Q: Back

Q: 2. Determine the positive real root of the function f(x) = In(x²) – 2 with initial guess [5/2, 3] us...

Q: An unforced, undamped Duffing equation (see web and Kreyszig §4.6 for applications) can be modelled ...

Q: E Quation: 13-0.2x+0.0015x2 Compare C'(400) with the cost of manufacturing the 401st yard of fabric....

A: We will calculate C'(x) from the given equation and then compare it with C(401)-C(400)

Question

Perform the given problem solving on Finite Divided Difference or Euler's method. Show the step-by-step solution with the numerical model, table of results, and graph of the model.