The dam cross section is an equilateral triangle, with a side length, L, of 50 m. Its width into the paper, b, is 100 m. The dam material has a specific gravity, SG, of 3.1. You may assume that the dam is loosely attached to the ground at its base, though there is significant friction to keep it from sliding.Is the weight of the dam sufficient to prevent it from tipping around its lower right corner?

Answers

Answer 1
Answer:

Answer:

Explanation:

In an equilateral trinagle the center of mass is at 1/3 of the height and horizontally centered.

We can consider that the weigth applies a torque of T = W*b/2 on the right corner, being W the weight and b the base of the triangle.

The weigth depends on the size and specific gravity.

W = 1/2 * b * h * L * SG

Then

Teq = 1/2 * b * h * L * SG * b / 2

Teq = 1/4 * b^2 * h * L * SG

The water would apply a torque of elements of pressure integrated over the area and multiplied by the height at which they are apllied:

T1 = \int\limits^h_0 {p(y) * sin(30) * L * (h-y)} \, dy

The term sin(30) is because of the slope of the wall

The pressure of water is:

p(y) = SGw * (h - y)

Then:

T1 = \int\limits^h_0 {SGw * (h-y) * sin(30) * L * (h-y)} \, dy

T1 = \int\limits^h_0 {SGw * sin(30) * L * (h-y)^2} \, dy

T1 = SGw * sin(30) * L * \int\limits^h_0 {(h-y)^2} \, dy

T1 = SGw * sin(30) * L * \int\limits^h_0 {(h-y)^2} \, dy

T1 = SGw * sin(30) * L * \int\limits^h_0 {h^2 - 2*h*y + y^2} \, dy

T1 = SGw * sin(30) * L * (h^2*y - h*y^2 + 1/3*y^3)(evaluated between 0 and h)

T1 = SGw * sin(30) * L * (h^2*h - h*h^2 + 1/3*h^3)

T1 = SGw * sin(30) * L * (h^3 - h^3 + 1/3*h^3)

T1 = 1/3 * SGw * sin(30) * L * h^3

To remain stable the equilibrant torque (Teq) must be of larger magnitude than the water pressure torque (T1)

1/4 * b^2 * h * L * SG > 1/3 * SGw * sin(30) * L * h^3

In an equilateral triangle h = b * cos(30)

1/4 * b^3 * cos(30) * L * SG  > 1/3 * SGw * sin(30) * L * b^3 * (cos(30))^3

SG > SGw * 4/3* sin(30) * (cos(30))^2

SG > 1/2 * SGw

For the dam to hold, it should have a specific gravity of at leas half the specific gravity of water.

This is avergae specific gravity, including holes.


Related Questions

As a means of preventing ice formation on the wings of a small, private aircraft, it is proposed that electric resistance heating elements be installed within the wings. To determine representative power requirements, consider nominal flight conditions for which the plane moves at 100 m/s in air that is at a temperature of -23 degree C. If the characteristic length of the airfoil is L = 2 m and wind tunnel measurements indicate an average friction coefficient of of C_f = 0.0025 for the nominal conditions, what is the average heat flux needed to maintain a surface temperature of T_s = 5 degree C?
Suppose there is a mobile application that can run in two modes: Lazy or Eager. In Lazy Mode, the execution time is 3.333 seconds. In Eager Mode, the app utilizes a faster timer resolution for its computations, so the execution time in Eager Mode is 2 seconds (i.e., Eager Mode execution time is 60% of Lazy Mode execution time).After finishing computation, the app sends some data to the cloud, regardless of the mode it’s in. The data size sent to the cloud is 600 MB. The bandwidth of communication is 15 MBps for WiFi and 5 MBps for 4G. Assume that the communication radio is idle during the computation time. Assume that the communication radio for WiFi has a power consumption of 75 mW when active and 15 mW when idle. Similarly, assume that the communication radio for 4G has a power consumption of 190 mW when active and 25 mW when idle. The Idle Power of the CPU is 7 mW, whereas the Active Power of the CPU is 5 mW per unit utilization. Assume that the power consumption of the CPU is a linear function of its utilization. In other words: P = (Idle Power) + (Utilization)*(Power per unit Utilization). A configuration of the mobile app involves choosing a timer resolution (Lazy or Eager) and choosing a type of radio (WiFi or 4G). For example, faster timer resolution (Eager) and 4G network is a configuration, while slower resolution (Lazy) and WiFi is another. There are four possible configurations in all.Required:What is the average power consumption for Eager WiFi, Lazy WiFi, Eager 4G, and Lazy 4G?
What is the difference between absolute and gage pressure?
If 100 J of heat is added to a system so that the final temperature of the system is 400 K, what is the change in entropy of the system? a)- 0.25 J/K b)- 2.5 J/K c)- 1 J/K d)- 4 J/K
When circuit switching is used, what is the maximum number of circuit-switched users that can be supported? Explain your answer in your own words.

Write a program that allows you to enter grocery item names into an array of strings and the cost of each item in an array of doubles. At the beginning of the program prompt the user to enter the total number of items they will be entering. Max value of 100. After entering the item names and cost, the application should display the names and cost and total cost of all items.

Answers

Answer:

#include <iostream>

#include <iomanip>

using namespace std;

int main(){

//declare arrays

string ItemName[100];

double ItemCost[100]={0.0};

//declare variable

string name="";

double Total=0.0;

int NumItems=0;

cout<<"Enter number of grocery item you will be entering";

cin>>NumItems

cout<<"\n";

if (NumItems>100)

{

  cout<<"Enter grocery items less than 100"

  cin>>NumItems

  cout<<"\n";

}

for (int i=1;i>=NumItems;i++)

{

  cout<<"Please enter the item name in one word only, Example:                                icecream\n";

  cin>>ItemName[i]

  cout<<"Please enter the cost as a decimal number, Example: 2.05\n\n";

  cin>>ItemCost[i];

}

cout<<"Items"<<"   "<<""$""<<"Cost"<<endl

for (int i=1;i>=NumItems;i++)

{

    cout<<ItemName[i]<<"   "<<"$"<<ItemCost[i]<<endl

}

for (int i=1;i>=NumItems;i++)

{

  Total=Total+ItemCost[i];

}

cout<<"Total:$"<<Total<<endl;

system("PAUSE");

return 0;

}

The structure of a house is such that it loses heat at a rate of 5400 kJ/h per degree Cdifference between the indoors and outdoors. A heat pump that requires a power input of 6 kW isused to maintain this house at 21 C. Determine the lowest outdoor temperature for which the heatpump can meet the heating requirements of this house

Answers

Answer: Tl = - 13.3°C

the lowest outdoor temperature is - 13.3°C

Explanation:

Given that;

Temperature of Th = 21°C = 21 + 273 = 294 K

the rate at which heat lost is Qh = 5400 kJ/h°C

the power input to heat pump Wnet = 6 kw

The COP of a reversible heat pump depends on the temperature limits in the cycle only, and is determined by;

COPhp = Th/(Th - Tl)

COPhp = Qh/Wnet

Qh/Wnet = Th/(Th -Tl)

the amount of heat loss is expressed as

Qh = 5400/3600(294 - Tl)

the temperature of sink

( 5400/3600(294 - Tl)) / 6 = 294 / ( 294 - Tl)

now solving the equation

Tl = 259.7 - 273

Tl = - 13.3°C

so the lowest outdoor temperature is - 13.3°C

Write two scnr.nextInt statements to get input values into birthMonth and birthYear. Then write a statement to output the month, a slash, and the year. End with newline. The program will be tested with inputs 1 2000 and then with inputs 5 1950. Ex: If the input is 1 2000, the output is: 1/2000

Answers

Answer:

import java.util.Scanner;

public class InputExample {

   public static void main(String[] args) {

       Scanner scnr = new Scanner(System.in);

       int birthMonth;

       int birthYear;

       birthMonth = scnr.nextInt();

       birthYear = scnr.nextInt();

       System.out.println(birthMonth+"/"+birthYear);

   }

}

import java.util.Scanner;

public class InputExample {

   public static void main(String[] args) {

       Scanner scnr = new Scanner(System.in);

       int birthMonth;

       int birthYear;

       // Get input values for birthMonth and birthYear from the user

       birthMonth = scnr.nextInt();

       birthYear = scnr.nextInt();

       // Output the month, a slash, and the year

       System.out.println(birthMonth + "/" + birthYear);

   }

}

When the program is tested with inputs 1 2000, the output will be:

1/2000

And when tested with inputs 5 1950, the output will be:

5/1950

Know more about java program:

brainly.com/question/34106786

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Water needs to be turned into steam in a high altitude lab where the atmospheric pressure is 84.6 KPa. Computte the heat energy (in calories) required to evaporate 900g of water at 15 degree C under these conditions.

Answers

Answer:

558.1918 kilocalories = 558191.8 calories

Explanation:

Data provided in the question:

Atmospheric pressure = 84.6 KPa

Mass of water, m = 900 g = 0.90 kg

Temperature = 15°C

Now,

Temperature at 84.6 KPa = 94.77°C

Therefore,

Heat energy required = m(CΔT + L)

here,

C is the specific heat of the water = 4.2 KJ/kg.°C

L = Latent heat of water = 2260 KJ/kg

Thus,

Heat energy required = 0.90[ 4.2 × (94.77 - 15) + 2260 ]

= 2335.53 KJ

also,

1 KJ = 0.239  Kilocalories

Therefore,

2335.53 KJ = 0.239 × 2335.53 Kilocalories

= 558.1918 kilocalories = 558191.8 calories

Automobiles must be able to sustain a frontal impact. Specifically, the design must allow low speed impacts with little damage, while allowing the vehicle front end structure to deform and absorb impact energy at higher speeds. Consider a frontal impact test of a vehicle with a mass of 1000 kg. a. For a low speed test (v = 2.5 m/s), compute the energy in the vehicle just prior to impact. If the bumper is a pure elastic element, what is the effective design stiffness required to limit the bumper maximum deflection during impact to 4 cm? b. At a higher speed impact of v = 25 m/s, considerable deformation occurs. To absorb the energy, the front end of a vehicle is designed to deform while providing a nearly constant force. For this condition, what is the amount of energy that must be absorbed by the deformation [neglecting the energy stored in the elastic deformation in (a)? If it is desired to limit the deformation to 10 cm, what level of resistance force is required? What is the deacceleration of the vehicle in this condition?

Answers

Answer:

Explanation:

The concept of Hooke's law was applied as it relates to deformation.

The detailed steps and appropriate substitution is as shown in the attached file.

The barrel of a bicycle tire pump becomes quite warm during use. Explain the mechanisms responsible for the temperature increase.

Answers

Answer:

The air heats up when being compressed and transefers heat to the barrel.

Explanation:

When a gas is compressed it raises in temperature. Assuming that the compression happens fast and is done before a significant amount of heat can be transferred to the barrel, we could say it is an adiabatic compression. This isn't exactly true, it is an approximation.

In an adiabatic transformation:

P^(1-k) * T^k = constant

For air k = 1.4

SO

P0^(-0.4) * T0^(1.4) = P1^(-0.4) * T1^(1.4)

T1^(1.4) = (P1^(0.4) * T0^(1.4))/(P0^(0.4))

T1^(1.4) = (P1)/(P0)^(0.4) * T0^(1.4)

T1 = T0 * (P1)/(P0)^(0.4/1.4)

T1 = T0 * (P1)/(P0)^(0.28)

SInce it is compressing, the fraction P1/P0 will always be greater than one, and raised to a positive fraction it will always yield a number greater than one, so the final temperature will be greater than the initial temperature.

After it was compressed the hot air will exchange heat with the barrel heating it up.