Suppose that a spherical droplet of liquid evaporates at a race that is proportional to its surface
Question:
Suppose that a spherical droplet of liquid evaporates at a race that is proportional to its surface area.
dV/dt = – kA
Where V = volume (mm3), t = time (h), k = the evaporation rater (mm/hr), and A = surface area (mm2). Use Euler’s method to compute the volume of the droplet from t = 0 to 10 min using a step size of 0.25 min. Assume that k = 0.1 mm/min and that the droplet initially has a radius of 3 mm. Assess the validity of your results by determining the radius of your final computed volume and verifying that it is consistent with the evaporation rate.
Step by Step Answer:
The volume of the droplet is related to the radius as This equation can be solved ...View the full answer
Numerical Methods For Engineers
ISBN: 9780071244299
5th Edition
Authors: Steven C. Chapra, Raymond P. Canale
Related Video
The area of a circle is given by the formula: A = ?r^2 Where A is the area, ? is a mathematical constant (approximately 3.14), and r is the radius of the circle. The radius is the distance from the center of the circle to the edge. So for example, if the radius of a circle is 5 units, the area would be: A = ?(5^2) = ?(25) = 78.5 square units Here three friends went out to a restaurant and decided to have pizza for lunch. While they were waiting for their order, one of them stepped out to take a call but promised to return in two minutes. The waiter came and presented them with the menu, and they decided to order two 10-inch pepperoni pizzas. The waiter took their order and left. Just then, the third friend returned and asked what they had ordered. They explained that they had ordered two small pepperoni pizzas as they were only three of them and it would be enough for them. However, the third friend suggested that for the same price, they could get a large pizza that would be much bigger than the two small ones. He asked the waiter for a pen and paper and proceeded to calculate the area of the two small pizzas and compared it to the area of one large pizza. The friends were amazed at how the circle measurements worked and decided to change their order from two small pizzas to one large pizza.
Students also viewed these Numerical Analysis questions
-
A snowball melts at a rate proportional to its surface area. (a) Show that its radius shrinks at a constant rate. (b) If it melts to 4 its original volume in one hour, how long will it take to melt...
-
A spherical droplet of water evaporates at a rate of 1 mm3 min. Find the rate of change of the radius when the droplet has a radius of 2.5 mm.
-
A spherical droplet of liquid A and radius ro evaporates into a stagnant layer of gas B. Derive an expression for the evaporation rate of species A in terms of the saturation pressure of species A,...
-
For a certain company, the cost function for producing x items is C(x)=30x+100 and the revenue function for selling x items is R(x)=0.5(x70)^2+2,450 . The maximum capacity of the company is 100...
-
There are data showing that smoking is detrimental to good health. Given that people could be helped and lives could be saved by reducing smoking, is it ethical to graph the data in a way that is...
-
Using De Morgan equivalent gates and bubble pushing methods, redraw the circuit in Figure 2.83 so that you can find the Boolean equation by inspection. Write the Boolean equation. B- C- D- E- Dor...
-
Selenelion Ltd is a small manufacturing business. For the year ending 30 June 2024, the company achieved sales of $2 772 000 and a gross profit margin of 30%. Although satisfied with this result,...
-
The finance director of the Bethandy Independent School District is making preliminary estimates of the budget outlook for the General Fund for the 20X8 fiscal year. These estimates will permit the...
-
How much would $ 1 , growing at 8 . 6 5 % per year, be worth after 8 5 years?
-
1 Carry out a five forces analysis of the advertising industry in 2015. What is the strength of the five forces and what underlying factors drive them? What is the industry attractiveness? 2 What are...
-
For the same storage tank described in Prob. 1.13, suppose that the outflow is not constant but rather depends on the depth. For this case, the differential equation for depth can be written as Use...
-
Newtons law of cooling says that the temperature of a body changes at a rate proportional to the difference between its temperature and that of the surrounding medium (the ambient temperature), dT/dt...
-
During 2011 outstanding common shares of General Electric (GE) decreased from 10,615,376,000 to 10,537,017,000. GE declared dividends of $6,458,000,000. The treasury stock account had a beginning...
-
Compare the margin contribution per product for the top and lowest performing team (highest & lowest amount of sales)?
-
What are the multifaceted implications of climate change on global sustainability efforts, and how do adaptation and mitigation strategies intersect with broader socio-economic and geopolitical...
-
In what ways do emerging technologies such as blockchain and distributed ledger systems facilitate enhanced transparency in supply chains, and what challenges do they pose in implementation and...
-
What role do economies of scale play in enhancing profit margins, and how can firms leverage them effectively ?
-
What is daily payroll if annual payroll is 244,458?
-
The goal of a security awareness program is to hold an individual accountable if they have not been instructed as to what is and is not acceptable with information security. A. True B. False
-
Accounting policies and practices that are most important to the portrayal of the companys financial condition and results, and require managements most difficult, subjective, or complex judgments...
-
Using the curved-arrow notation, fill in the details for base-catalyzed mutarotation of glucopyranose. Begin by removing a proton from the hydroxy group at carbon-1.
-
Use Gauss elimination to solve: 8x 1 + 2x 2 2x 3 = 22 10x 1 + 2x 2 + 4x 3 = 4 12x 1 + 2x 2 + 2x 3 = 6 Employ partial pivoting and check your answers by substituting them into the original equations.
-
Determine the Frobenius and the row-sum norms for the systems in Probs. 10.3 and 10.4. Scale the matrices by making the maximum element in each row equal to one?
-
Perform Crout decomposition on 2x1 - 5x2 + x3 = 12 -x1 + 3x2 - x3 = -8 3x1 - 4x2 + 2x3 = 16 Then, multiply the resulting [L] and [U] matrices to determine that [A] is produced?
-
S&J Catering is a small catering business operating in Western Sydney. Business partners, Jack and Simon, established the business a year ago. To start up the business, the partners contributed...
-
In 20X1, Lee was hurt in the course of his employment with Foster Farms. In 20X1, Lee was paid the following amounts from Foster Farms' worker's compensation insurance company: $30,000 for a physical...
-
Briefly describe tax administrative matters including: Tax collection and withholding mechanisms (PAYG withholding, PAYG instalments).
Study smarter with the SolutionInn App