Answer:
![\eta =\dfrac{(h_3-h_4)-(h_2-h_1)}{(h_3-h_5)}](https://tex.z-dn.net/?f=%5Ceta%20%3D%5Cdfrac%7B%28h_3-h_4%29-%28h_2-h_1%29%7D%7B%28h_3-h_5%29%7D)
Explanation:
generally regeneration of cycle is used in the case of gas turbine. due to regeneration efficiency of turbine is increased but there is no effect on the on the net work out put of turbine.Actually in regeneration net heta input is decreases that is why total efficiency increase.
Now from T-S diagram
![W_{net}=W_{out}-W_{in}](https://tex.z-dn.net/?f=W_%7Bnet%7D%3DW_%7Bout%7D-W_%7Bin%7D)
![W_{net}=(h_3-h_4)-(h_2-h_1)](https://tex.z-dn.net/?f=W_%7Bnet%7D%3D%28h_3-h_4%29-%28h_2-h_1%29)
![Q_{in}=h_3-h_5](https://tex.z-dn.net/?f=Q_%7Bin%7D%3Dh_3-h_5)
Due to generation
amount of energy has been saved.
![Q_{generation}=Q_{saved}](https://tex.z-dn.net/?f=Q_%7Bgeneration%7D%3DQ_%7Bsaved%7D)
So efficiency of cycle ![\eta =\frac{W_{net}}{Q_{in}}](https://tex.z-dn.net/?f=%5Ceta%20%3D%5Cfrac%7BW_%7Bnet%7D%7D%7BQ_%7Bin%7D%7D)
![\eta =\dfrac{(h_3-h_4)-(h_2-h_1)}{(h_3-h_5)}](https://tex.z-dn.net/?f=%5Ceta%20%3D%5Cdfrac%7B%28h_3-h_4%29-%28h_2-h_1%29%7D%7B%28h_3-h_5%29%7D)
Effectiveness of re-generator
![\varepsilon =\dfrac{(h_5-h_2)}{(h_4-h_2)}](https://tex.z-dn.net/?f=%5Cvarepsilon%20%3D%5Cdfrac%7B%28h_5-h_2%29%7D%7B%28h_4-h_2%29%7D)
So the efficiency of regenerative cycle
![\eta =\dfrac{(h_3-h_4)-(h_2-h_1)}{(h_3-h_5)}](https://tex.z-dn.net/?f=%5Ceta%20%3D%5Cdfrac%7B%28h_3-h_4%29-%28h_2-h_1%29%7D%7B%28h_3-h_5%29%7D)
Answer:
Explanation:
Since there are six points, the minimum distance from all points would be the centroid of polygon formed by A,B,C,D,E,F
To find the coordinates of centroid of a polygon we use the following formula. Let A be area of the polygon.
where i=1 to N-1 and N=6
A area of the polygon can be found by the following formula
where i=1 to N-1
![A=\frac{1}{2}[ (x_{1} y_{2} -x_{2} y_{1})+ (x_{2} y_{3} -x_{3} y_{2})+(x_{3} y_{4} -x_{4} y_{3})+(x_{4} y_{5} -x_{5} y_{4})+(x_{5} y_{6} -x_{6} y_{5})]](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%5B%20%28x_%7B1%7D%20%20y_%7B2%7D%20-x_%7B2%7D%20%20y_%7B1%7D%29%2B%20%28x_%7B2%7D%20%20y_%7B3%7D%20-x_%7B3%7D%20%20y_%7B2%7D%29%2B%28x_%7B3%7D%20%20y_%7B4%7D%20-x_%7B4%7D%20%20y_%7B3%7D%29%2B%28x_%7B4%7D%20%20y_%7B5%7D%20-x_%7B5%7D%20%20y_%7B4%7D%29%2B%28x_%7B5%7D%20%20y_%7B6%7D%20-x_%7B6%7D%20%20y_%7B5%7D%29%5D)
A=0.5[(20×25 -25×15) +(25×32 -13×25)+(13×21 -4×32)+(4×8 -18×21)+(18×14 -25×8)
A=225.5 miles²
Now putting the value of area in Cx and Cy
![C_{x} =\frac{1}{6A}[ [(x_{1}+x_{2})(x_{1} y_{2} -x_{2} y_{1})]+ [(x_{2}+x_{3})(x_{2} y_{3} -x_{3} y_{2})]+[(x_{3}+x_{4})(x_{3} y_{4} -x_{4} y_{3})]+[(x_{4}+x_{5})(x_{4} y_{5} -x_{5} y_{4})]+[(x_{5}+x_{6})(x_{5} y_{6} -x_{6} y_{5})]]](https://tex.z-dn.net/?f=C_%7Bx%7D%20%3D%5Cfrac%7B1%7D%7B6A%7D%5B%20%5B%28x_%7B1%7D%2Bx_%7B2%7D%29%28x_%7B1%7D%20%20y_%7B2%7D%20-x_%7B2%7D%20%20y_%7B1%7D%29%5D%2B%20%5B%28x_%7B2%7D%2Bx_%7B3%7D%29%28x_%7B2%7D%20%20y_%7B3%7D%20-x_%7B3%7D%20%20y_%7B2%7D%29%5D%2B%5B%28x_%7B3%7D%2Bx_%7B4%7D%29%28x_%7B3%7D%20%20y_%7B4%7D%20-x_%7B4%7D%20%20y_%7B3%7D%29%5D%2B%5B%28x_%7B4%7D%2Bx_%7B5%7D%29%28x_%7B4%7D%20%20y_%7B5%7D%20-x_%7B5%7D%20%20y_%7B4%7D%29%5D%2B%5B%28x_%7B5%7D%2Bx_%7B6%7D%29%28x_%7B5%7D%20%20y_%7B6%7D%20-x_%7B6%7D%20%20y_%7B5%7D%29%5D%5D)
putting the values of x's and y's you will get
![C_{x} =15.36](https://tex.z-dn.net/?f=C_%7Bx%7D%20%3D15.36)
For Cy
![C_{y} =\frac{1}{6A}[ [(y_{1}+y_{2})(x_{1} y_{2} -x_{2} y_{1})]+ [(y_{2}+y_{3})(x_{2} y_{3} -x_{3} y_{2})]+[(y_{3}+y_{4})(x_{3} y_{4} -x_{4} y_{3})]+[(y_{4}+y_{5})(x_{4} y_{5} -x_{5} y_{4})]+[(y_{5}+y_{6})(x_{5} y_{6} -x_{6} y_{5})]]](https://tex.z-dn.net/?f=C_%7By%7D%20%3D%5Cfrac%7B1%7D%7B6A%7D%5B%20%5B%28y_%7B1%7D%2By_%7B2%7D%29%28x_%7B1%7D%20%20y_%7B2%7D%20-x_%7B2%7D%20%20y_%7B1%7D%29%5D%2B%20%5B%28y_%7B2%7D%2By_%7B3%7D%29%28x_%7B2%7D%20%20y_%7B3%7D%20-x_%7B3%7D%20%20y_%7B2%7D%29%5D%2B%5B%28y_%7B3%7D%2By_%7B4%7D%29%28x_%7B3%7D%20%20y_%7B4%7D%20-x_%7B4%7D%20%20y_%7B3%7D%29%5D%2B%5B%28y_%7B4%7D%2By_%7B5%7D%29%28x_%7B4%7D%20%20y_%7B5%7D%20-x_%7B5%7D%20%20y_%7B4%7D%29%5D%2B%5B%28y_%7B5%7D%2By_%7B6%7D%29%28x_%7B5%7D%20%20y_%7B6%7D%20-x_%7B6%7D%20%20y_%7B5%7D%29%5D%5D)
putting the values of x's and y's you will get
![C_{y} =22.55](https://tex.z-dn.net/?f=C_%7By%7D%20%3D22.55)
So coordinates for the fire station should be (15.36,22.55)
Answer:
11.2mm or 0.45in
Explanation:
The percent cold work, attendant tensile strength and ductility if drawing is carried out without interruption is given by the equation you will find in the attached file.
Please go through the attached file for a step by step solution to this question.