Explanation Given: The given equation is d h d t = − c A h A w 2 g h . Calculation: Consider the equation. d h d t = − A h A w 2 g h (1) Where A w is cross sectional area of water and condition is h ( 0 ) = H . Now. d h d t = − A h A w 2 g h d h 2 g h = − A h A w d t Integrate both sides. ∫ d h 2 g h = − A h A w ∫ d t 1 2 g 2 2 g h = − A h A w t + c 1 g 2 g h = − A h A w t + c Put t = 0 and h = H . 1 32 2 × 32 H = ( − A h A w × 0 ) + c c = 1 32 64 H c = H 4 Put the value of c in above equation To determine (b) To find: Time required to empty the tank.

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 2.8, Problem 13E

To determine

(a)

To find: The solution of the differential equation and sketch the graph of h(t).

To determine

(b)

To find: Time required to empty the tank.

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Chapter 2.8, Problem 12E

Chapter 2.8, Problem 14E

Chapter 2 Solutions

Advanced Engineering Mathematics

Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

Ch. 2.1 - Prob. 11E Ch. 2.1 - Prob. 12E Ch. 2.1 - Prob. 13E Ch. 2.1 - Prob. 14E Ch. 2.1 - Prob. 15E Ch. 2.1 - Prob. 16E Ch. 2.1 - Prob. 19E Ch. 2.1 - Prob. 20E Ch. 2.1 - Prob. 21E Ch. 2.1 - Prob. 22E Ch. 2.1 - Prob. 23E Ch. 2.1 - Prob. 24E Ch. 2.1 - Prob. 25E Ch. 2.1 - Prob. 26E Ch. 2.1 - Prob. 27E Ch. 2.1 - Prob. 28E Ch. 2.1 - Prob. 29E Ch. 2.1 - Prob. 30E Ch. 2.1 - Prob. 31E Ch. 2.1 - Prob. 32E Ch. 2.1 - Prob. 33E Ch. 2.1 - Prob. 34E Ch. 2.1 - Prob. 35E Ch. 2.1 - Prob. 36E Ch. 2.1 - Prob. 37E Ch. 2.1 - Prob. 38E Ch. 2.1 - Prob. 39E Ch. 2.1 - Prob. 40E Ch. 2.1 - Prob. 41E Ch. 2.1 - Prob. 42E Ch. 2.2 - Prob. 1E Ch. 2.2 - Prob. 2E Ch. 2.2 - Prob. 3E Ch. 2.2 - Prob. 4E Ch. 2.2 - Prob. 5E Ch. 2.2 - Prob. 6E Ch. 2.2 - Prob. 7E Ch. 2.2 - Prob. 8E Ch. 2.2 - Prob. 9E Ch. 2.2 - Prob. 10E Ch. 2.2 - Prob. 11E Ch. 2.2 - Prob. 12E Ch. 2.2 - Prob. 13E Ch. 2.2 - Prob. 14E Ch. 2.2 - Prob. 15E Ch. 2.2 - Prob. 16E Ch. 2.2 - Prob. 17E Ch. 2.2 - Prob. 18E Ch. 2.2 - Prob. 19E Ch. 2.2 - Prob. 20E Ch. 2.2 - 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Tsunami Waves and BreakwatersThis is a continuation of Exercise 16. Breakwaters affect wave height by reducing energy. See Figure 5.30. If a tsunami wave of height H in a channel of width W encounters a breakwater that narrows the channel to a width w, then the height h of the wave beyond the breakwater is given by h=HR0.5, where R is the width ratio R=w/W. a. Suppose a wave of height 8 feet in a channel of width 5000feet encounters a breakwater that narrows the channel to 3000feet. What is the height of the wave beyond the breakwater? b. If a channel width is cut in half by a breakwater, what is the effect on wave height? 16. Height of Tsunami WavesWhen waves generated by tsunamis approach shore, the height of the waves generally increases. Understanding the factors that contribute to this increase can aid in controlling potential damage to areas at risk. Greens law tells how water depth affects the height of a tsunami wave. If a tsunami wave has height H at an ocean depth D, and the wave travels to a location with water depth d, then the new height h of the wave is given by h=HR0.25, where R is the water depth ratio given by R=D/d. a. Calculate the height of a tsunami wave in water 25feet deep if its height is 3feet at its point of origin in water 15,000feet deep. b. If water depth decreases by half, the depth ratio R is doubled. How is the height of the tsunami wave affected?

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03a: Numerical Differentiation Review; Author: Jaisohn Kim;https://www.youtube.com/watch?v=IMYsqbV4CEg;License: Standard YouTube License, CC-BY

(a) To find: The solution of the differential equation and sketch the graph of h ( t ) .

Solution Summary: The author explains the solution of the differential equation and the graph of h(t).

Videos

(a)

To find: The solution of the differential equation and sketch the graph of h(t).

(b)

To find: Time required to empty the tank.

Want to see the full answer?

Chapter 2 Solutions

(a) To find: The solution of the differential equation and sketch the graph of h ( t ) .

Solution Summary: The author explains the solution of the differential equation and the graph of h(t).

Videos

(a) To find: The solution of the differential equation and sketch the graph of h(t).

(b) To find: Time required to empty the tank.

Want to see the full answer?

Chapter 2 Solutions

(a)

To find: The solution of the differential equation and sketch the graph of h(t).

(b)

To find: Time required to empty the tank.