A water supply agency is planning to add two reservoirs to its system. Water will flow from Reservoir A to Reservoir B via a 10,
000-ft-long, 24-inch diameter steel pipe. The pipe will be installed beneath a road between the two reservoirs. The road crosses over a hill with a summit elevation of 375 ft above MSL. This summit is at a distance of 3000 ft from reservoir A.The elevation of the water surface in reservoir A will vary between 348.0 and 362.0 ft above MSL and the water surface in reservoir B will vary between 244.1 and 255.4 ft above MSL.Assume a temperature of 50°F. Neglect minor losses. Use a Hazen-Williams friction factor of 100 and an equivalent sand grain roughness of 0.060 in. These values are from Table 12.1.1 in the text.(a) Make a sketch that defines the geometry of the problem. Clearly label dimensions.(b) Determine which water level combination will lead to maximum discharge in the pipe and which water level combination will lead to minimum discharge in the pipe. This should be done by analyzing the relevant equations without doing any calculations. Show your work and explain your logic.
1 answer:
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Let <em>f(z)</em> = (4<em>z </em>² + 2<em>z</em>) / (2<em>z </em>² - 3<em>z</em> + 1).
First, carry out the division:
<em>f(z)</em> = 2 + (8<em>z</em> - 2) / (2<em>z </em>² - 3<em>z</em> + 1)
Observe that
2<em>z </em>² - 3<em>z</em> + 1 = (2<em>z</em> - 1) (<em>z</em> - 1)
so you can separate the rational part of <em>f(z)</em> into partial fractions. We have
(8<em>z</em> - 2) / (2<em>z </em>² - 3<em>z</em> + 1) = <em>a</em> / (2<em>z</em> - 1) + <em>b</em> / (<em>z</em> - 1)
8<em>z</em> - 2 = <em>a</em> (<em>z</em> - 1) + <em>b</em> (2<em>z</em> - 1)
8<em>z</em> - 2 = (<em>a</em> + 2<em>b</em>) <em>z</em> - (<em>a</em> + <em>b</em>)
so that <em>a</em> + 2<em>b</em> = 8 and <em>a</em> + <em>b</em> = 2, yielding <em>a</em> = -4 and <em>b</em> = 6.
So we have
<em>f(z)</em> = 2 - 4 / (2<em>z</em> - 1) + 6 / (<em>z</em> - 1)
or
<em>f(z)</em> = 2 - (2/<em>z</em>) (1 / (1 - 1/(2<em>z</em>))) + (6/<em>z</em>) (1 / (1 - 1/<em>z</em>))
Recall that for |<em>z</em>| < 1, we have
Replace <em>z</em> with 1/<em>z</em> to get
so that by substitution, we can write
Now condense <em>f(z)</em> into one series:
So, the inverse <em>Z</em> transform of <em>f(z)</em> is .
Answer:
hello your question has a missing part below is the missing part
Consider the string length equal to
answer : 2cos(2t) sin(2x) - 10cos(10t)sin(10x)
Explanation:
Given string length =
distorted function f(x) = 2sin(2x) - 10sin(10x)
Determine the wave formed in the string
attached below is a detailed solution of the problem
Answer:
// Scanner class is imported to allow program
// receive input
import java.util.Scanner;
// RomanNumerals class is defined
public class RomanNumerals {
// main method that signify beginning of program execution
public static void main(String args[]) {
// Scanner object scan is created
// it receive input via keyboard
Scanner scan = new Scanner(System.in);
// Prompt is display asking the user to enter number
System.out.println("Enter your number: ");
// the user input is stored at numberOfOrder
int number = scan.nextInt();
// switch statement which takes number as argument
// the switch statement output the correct roman numeral
// depending on user input
switch(number){
case 1:
System.out.println("I");
break;
case 2:
System.out.println("II");
break;
case 3:
System.out.println("III");
break;
case 4:
System.out.println("IV");
break;
case 5:
System.out.println("V");
break;
case 6:
System.out.println("VI");
break;
case 7:
System.out.println("VII");
break;
case 8:
System.out.println("VIII");
break;
case 9:
System.out.println("IX");
break;
case 10:
System.out.println("X");
break;
// this part is executed if user input is not between 1 to 10
default:
System.out.println("Error. Number must be between 1 - 10.");
}
}
}
Explanation:
The program is well commented. A sample image of program output is attached.
The switch statement takes the user input (number) as argument as it goes through each case block in the switch statement and match with the corresponding case to output the roman version of that number. If the number is greater 10 or less than 1; the default block is executed and it display an error message telling the user that number must be between 1 - 10.
