Answer:
A) m' = 351.49 kg/s
B) m'= 1036.91 kg/s
Explanation:
We are given;
Pressure Ratio;r_p = 12
Inlet temperature of compressor;T1 = 300 K
Inlet temperature of turbine;T3 = 1000 K
cp = 1.005 kJ/kg·K
k = 1.4
Net power output; W' = 70 MW = 70000 KW
A) Now, the formula for the mass flow rate using the total power output of the compressor and turbine is given as;
m' = W'/[cp(T3(1 - r_p^(-(k - 1)/k)) - T1(r_p^((k - 1)/k))
At, 100% efficiency, plugging in the relevant values, we have;
m' = 70000/(1.005(1000(1 - 12^(-(1.4 - 1)/1.4)) - 300(12^((1.4 - 1)/1.4)))
m' = 70000/199.1508
m' = 351.49 kg/s
B) At 85% efficiency, the formula will now be;
m' = W'/[cp(ηT3(1 - r_p^(-(k - 1)/k)) - (T1/η) (r_p^((k - 1)/k))
Where η is efficiency = 0.85
Thus;
m' = 70000/(1.005(0.85*1000(1 - 12^(-(1.4 - 1)/1.4)) - (300/0.85)(12^((1.4 - 1)/1.4)))
m' = 70000/(1.005*(432.09129 - 364.9189)
m'= 1036.91 kg/s
Answer:
1) Dimensions of shear rate is ![[T^{-1}]](https://tex.z-dn.net/?f=%5BT%5E%7B-1%7D%5D)
.
2)Dimensions of shear stress are ![[ML^{-1}T^{-2}]](https://tex.z-dn.net/?f=%5BML%5E%7B-1%7DT%5E%7B-2%7D%5D)
Explanation:
Since the dimensions of velocity 'v' are ![[LT^{-1}]](https://tex.z-dn.net/?f=%5BLT%5E%7B-1%7D%5D)
and the dimensions of distance 'y' are ![[L]](https://tex.z-dn.net/?f=%5BL%5D)
, thus the dimensions of 
become
![\frac{[LT^{-1}]}{[L]}=[T^{-1}]](https://tex.z-dn.net/?f=%5Cfrac%7B%5BLT%5E%7B-1%7D%5D%7D%7B%5BL%5D%7D%3D%5BT%5E%7B-1%7D%5D)
and hence the units become 
.
Now we know that the dimensions of coefficient of dynamic viscosity 
are ![[ML^{-1}T^{-1}]](https://tex.z-dn.net/?f=%5BML%5E%7B-1%7DT%5E%7B-1%7D%5D)
thus the dimensions of shear stress can be obtained from the given formula as
![[\tau ]=[ML^{-1}T^{-1}]\times [T^{-1}]\\\\[\tau ]=[ML^{-1}T^{-2}]](https://tex.z-dn.net/?f=%5B%5Ctau%20%5D%3D%5BML%5E%7B-1%7DT%5E%7B-1%7D%5D%5Ctimes%20%5BT%5E%7B-1%7D%5D%5C%5C%5C%5C%5B%5Ctau%20%5D%3D%5BML%5E%7B-1%7DT%5E%7B-2%7D%5D)
Now we know that dimensions of momentum are ![[MLT^{-1}]](https://tex.z-dn.net/?f=%5BMLT%5E%7B-1%7D%5D)
The dimensions of 
are ![[L^{2}T]](https://tex.z-dn.net/?f=%5BL%5E%7B2%7DT%5D)
Thus the dimensions of ![\frac{Moumentum}{Area\times time}=\frac{MLT^{-1}}{L^{2}T}=[MLT^{-2}]](https://tex.z-dn.net/?f=%5Cfrac%7BMoumentum%7D%7BArea%5Ctimes%20time%7D%3D%5Cfrac%7BMLT%5E%7B-1%7D%7D%7BL%5E%7B2%7DT%7D%3D%5BMLT%5E%7B-2%7D%5D)
Which is same as that of shear stress. Hence proved.
I think D. By pressing gradually
Answer:
<em>55%</em>
Explanation:
hot reservoir = 1100 K
cold reservoir = 500 K
<em>This is a Carnot system</em>
For a Carnot system, maximum efficicency of the system is given as
Eff = 1 - 
where Tc = temperature of cold reservoir = 500K
Th = temperature of hot reservoir = 1100 K
Eff = 1 - 
Eff = 1 - 0.45 = 0.55 or<em> 55%</em>
Answer:
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