Consider a water tank with a hole of area a in its base. The tank will...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Consider a water tank with a hole of area a in its base. The tank will drain through this hole, at a rate proportional to the height of the water (as this influences the pressure). Torricelli's Law describes this process: dh 2gh(t). dt where: h(t) = the height of water in the tank at time t in m, • A = is the cross-sectional area of the tank in m?, • a = the area of the hole in the bottom of the tank in m2, and g = 9.81 m/s is the acceleration due to gravity. For the following questions, use A = 10 m², a = 0.1 m?, and h(0) = 10 m. 1. Solve the ODE using separation of variables. 2. Use a first order Taylor series to show that when Torricelli's law is linearised about the initial height, we get dh a AV 2h(0) (h(t) + h(0)) dt 3. Solve the linearised ODE using the integrating factor method. 4. Plot your solutions to Q1 and Q3 in the same figure. Discuss the accuracy of the linearised ODE solution. Consider a water tank with a hole of area a in its base. The tank will drain through this hole, at a rate proportional to the height of the water (as this influences the pressure). Torricelli's Law describes this process: dh 2gh(t). dt where: h(t) = the height of water in the tank at time t in m, • A = is the cross-sectional area of the tank in m?, • a = the area of the hole in the bottom of the tank in m2, and g = 9.81 m/s is the acceleration due to gravity. For the following questions, use A = 10 m², a = 0.1 m?, and h(0) = 10 m. 1. Solve the ODE using separation of variables. 2. Use a first order Taylor series to show that when Torricelli's law is linearised about the initial height, we get dh a AV 2h(0) (h(t) + h(0)) dt 3. Solve the linearised ODE using the integrating factor method. 4. Plot your solutions to Q1 and Q3 in the same figure. Discuss the accuracy of the linearised ODE solution.
Expert Answer:
Related Book For
Posted Date:
Students also viewed these accounting 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 population is growing at a rate proportional to its size. After 5 years, the population size was 164000. After 12 years, the population size was 235000. What was the original population size?
-
A bacterial population grows at a rate proportional to its size. Initially, it is 10000, and after 10days it is 20000. What is the population after 25 days?
-
Which of the theoretical approaches are the most useful in explaining your organisations current IHRM policies and practices?
-
Why do most people resist change?
-
1. What were the motivation(s) for Greyston Bakerys diversifications? 2. Referring to the Ansoff matrix, how would you classify these diversifications?
-
What are the three components of an Expert System (ES) program? Explain what each component does.
-
Mazurka Corporation has 2,000 shares of $100, 8 percent cumulative preferred stock outstanding and 40,000 shares of $1 par value common stock outstanding. In the companys first three years of...
-
1. How are Michael Porter's forces defined, according to what you have observed in the video? 2. Mention and explain what Michael Porter's 5 forces are. 3. Are there companies in which Michael...
-
A binary mixture of mole fraction zj is flashed (o conditions T and P, Fur one of the following determine: the equilibrium mole fractions x1 and y1 of the liquid and vapor phases formed, the molar...
-
On 01 July 2016, Aiden Limited decided to change its accounting policy in order to expense finance costs as a period cost instead of capitalising them as was previously done. The effect of this...
-
The assumption that the effects of transactions and other events are recognized when they occur, not when the cash flows occur, is called: A. relevance. B. accrual basis. C. going concern.
-
A financial analyst is analyzing the amortization of a product patent acquired by MAKETTI S.p.A., an Italian corporation. He gathers the following information about the patent: If the analyst uses...
-
Accrued expenses (accrued liabilities) are: A. expenses that have been paid. B. created when another liability is reduced. C. expenses that have been reported on the income statement but not yet paid.
-
Which of the following elements represents an economic resource? A. Asset. B. Liability. C. Owners equity.
-
A companys profitability for a period would best be evaluated using the: A. balance sheet. B. income statement. C. statement of cash flows.
-
Design a comprehensive communication strategy for a multinational corporation (MNC) that aims to rebrand its image and reposition itself as a socially responsible and environmentally conscious...
-
The slopes of the tangents at the points where the curve y = x2 - 4x intersects the X-axis is 1) 1 2) +2 3) +3 4) +4
-
A spherical steel ball rests at the bottom of the tank of Problem 21. Answer the question posed there if the ball has radius (a) 6 inches (b) 2 feet. (Assume that the ball does not affect the flow...
-
Find the length of the curve given parametrically by x = et sint, y = et cos t, 0 t .
-
In problem 1-3, find (depending on ) so that the given implication is true. 1. |x - 5| < |3x - 15| < 2. |x - 2| < |4x - 8| < 3. |x + 6| < |6x + 36| <
-
The duties of a nozzle and a diffuser are (a) Opposite to each other (b) Identical to each other (c) Not comparable at all (d) None of these.
-
Nozzles and diffusers are widely used in (a) Heat exchangers (b) Refrigeration systems (c) Rockets and other space vehicles (d) None of these.
-
Pick out the correct relation between the \(\mathrm{COP}\) of a refrigerator \(\left(\mathrm{COP}_{\mathrm{R}} ight)\) and that of the heat pump \(\left(\mathrm{COP}_{\mathrm{HP}} ight)\) (a)...
Study smarter with the SolutionInn App