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yanalaym [24]
3 years ago
11

A rectangular region ABCD is to be built inside a semicircle of radius 10 m with points A and B on the line for the diameter and

points C and D on the semicircle with CD parallel to AB. The objective is to find the height h * that maximizes the area of ABCD.
Formulate the optimization problem.
Engineering
1 answer:
Talja [164]3 years ago
7 0

Answer:A rectangular region ABCD is to be built inside a semicircle of radius 10 m with points A and B on the line for the diameter and points C and D on the semicircle with CD parallel to AB. The objective is to find the height h * that maximizes the area of ABCD.

Formulate the optimization problem.

Explanation:A rectangular region ABCD is to be built inside a semicircle of radius 10 m with points A and B on the line for the diameter and points C and D on the semicircle with CD parallel to AB. The objective is to find the height h * that maximizes the area of ABCD.

Formulate the optimization problem.

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Steam at 4 MPa and 350°C is expanded in an adiabatic turbine to 125kPa. What is the isentropic efficiency (percent) of this turb
guajiro [1.7K]

Answer:

\eta_{turbine} = 0.603 = 60.3\%

Explanation:

First, we will find actual properties at given inlet and outlet states by the use of steam tables:

AT INLET:

At 4MPa and 350°C, from the superheated table:

h₁ = 3093.3 KJ/kg

s₁ = 6.5843 KJ/kg.K

AT OUTLET:

At P₂ = 125 KPa and steam is saturated in  vapor state:

h₂ = h_{g\ at\ 125KPa} = 2684.9 KJ/kg

Now, for the isentropic enthalpy, we have:

P₂ = 125 KPa and s₂ = s₁ = 6.5843 KJ/kg.K

Since s₂ is less than s_g and greater than s_f at 125 KPa. Therefore, the steam is in a saturated mixture state. So:

x = \frac{s_2-s_f}{s_{fg}} \\\\x = \frac{6.5843\ KJ/kg.K - 1.3741\ KJ/kg.K}{5.91\ KJ/kg.K}\\\\x = 0.88

Now, we will find h_{2s}(enthalpy at the outlet for the isentropic process):

h_{2s} = h_{f\ at\ 125KPa}+xh_{fg\ at\ 125KPa}\\\\h_{2s} = 444.36\ KJ/kg + (0.88)(2240.6\ KJ/kg)\\h_{2s} = 2416.088\ KJ/kg

Now, the isentropic efficiency of the turbine can be given as follows:

\eta_{turbine} = \frac{h_1-h_2}{h_1-h_{2s}}\\\\\eta_{turbine} = \frac{3093.3\ KJ/kg-2684.9\ KJ/kg}{3093.3\ KJ/kg-2416.088\ KJ/kg}\\\\\eta_{turbine} = \frac{408.4\ KJ/kg}{677.212\ KJ/kg}\\\\\eta_{turbine} = 0.603 = 60.3\%

3 0
3 years ago
A 132mm diameter solid circular section​
Ganezh [65]

Answer:

not sure if this helps but

5 0
3 years ago
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
lisabon 2012 [21]

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.

6 0
2 years ago
When you learned about the Highway Transportation system you learned about 6 different types of people as
Musya8 [376]

Answer: 3 different types of people using Highway Transportation system are :

1. Pedestrians - should be given priority while driving.

2. Cyclists - should be given enough space on road.

3. Motorcyclists- should be given enough space on road.

Explanation:

1. Pedestrians - Most of pedestrians use to walk on the footpath along side road that keeps them on a safe side. But there are places without footpath along side road, in that case they have to walk on the road itself. Here, we need to take care for them. We need to wait in case they are crossing road and also check for them while taking a turn.

2. Cyclists - They travel on road but are tough to figure out. They travel at a slower pace compared to cars. To avoid any accident with them, we are supposed to give them enough space which should be equivalent to a car's space.

3. Motorcyclists - They can pass by very closely and also come between lanes. Most of the things to be considered here are same as that of cyclists. Here also, we need to check for them carefully while taking a turn. Also, need to give them enough space.

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3 years ago
Create a flowchart that describes the following algorithm and then write Python code to implement the algorithm. Write the Pytho
Naya [18.7K]

Answer:

<em>Python code is as follows: </em>

********************************************************************************

#function to get number up to any number of decimal places

def toFixed(value, digits):

return "%.*f" % (digits, value)

print("Enter the price: ", end='', flush=True) #prompt for the input of price

price = float(input()) #taken input

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print("Total Cost after the sales tax of 5% is applied: " + toFixed(totalCost,2)) #print and output totalCost

************************************************************************************

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3 years ago
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