Answer:
Pressure = 115.6 psia
Explanation:
Given:
v=800ft/s
Air temperature = 10 psia
Air pressure = 20F
Compression pressure ratio = 8
temperature at turbine inlet = 2200F
Conversion:
1 Btu =775.5 ft lbf,
= 32.2 lbm.ft/lbf.s², 1Btu/lbm=25037ft²/s²
Air standard assumptions:
= 0.0240Btu/lbm.°R, R = 53.34ft.lbf/lbm.°R = 1717.5ft²/s².°R 0.0686Btu/lbm.°R
k= 1.4
Energy balance:
As enthalpy exerts more influence than the kinetic energy inside the engine, kinetic energy of the fluid inside the engine is negligible
hence ![v_{a} ^{2} = 0](https://tex.z-dn.net/?f=v_%7Ba%7D%20%5E%7B2%7D%20%3D%200)
![h_{1} + \frac{v_{1} ^{2} }{2} = h_{a} \\h_{1} -h_{a} = - \frac{v_{1} ^{2} }{2} \\ c_{p} (T_{1} -T_{a})= - \frac{v_{1} ^{2} }{2} \\(T_{1} -T_{a}) = - \frac{v_{1} ^{2} }{2c_{p} }\\ T_{a}=T_{1} + \frac{v_{1} ^{2} }{2c_{p} }](https://tex.z-dn.net/?f=h_%7B1%7D%20%2B%20%5Cfrac%7Bv_%7B1%7D%20%5E%7B2%7D%20%7D%7B2%7D%20%3D%20h_%7Ba%7D%20%5C%5Ch_%7B1%7D%20-h_%7Ba%7D%20%3D%20-%20%5Cfrac%7Bv_%7B1%7D%20%5E%7B2%7D%20%7D%7B2%7D%20%5C%5C%20c_%7Bp%7D%20%28T_%7B1%7D%20-T_%7Ba%7D%29%3D%20-%20%5Cfrac%7Bv_%7B1%7D%20%5E%7B2%7D%20%7D%7B2%7D%20%5C%5C%28T_%7B1%7D%20-T_%7Ba%7D%29%20%3D%20-%20%5Cfrac%7Bv_%7B1%7D%20%5E%7B2%7D%20%7D%7B2c_%7Bp%7D%20%7D%5C%5C%20T_%7Ba%7D%3DT_%7B1%7D%20%2B%20%20%5Cfrac%7Bv_%7B1%7D%20%5E%7B2%7D%20%7D%7B2c_%7Bp%7D%20%7D)
= 20+460 = 480°R
= 533.25°R
Pressure at the inlet of compressor at isentropic condition
![P_{a } =P_{1}(\frac{T_{a} }{T_{1} }) ^{k/(k-1)}](https://tex.z-dn.net/?f=P_%7Ba%20%7D%20%3DP_%7B1%7D%28%5Cfrac%7BT_%7Ba%7D%20%7D%7BT_%7B1%7D%20%7D%29%20%5E%7Bk%2F%28k-1%29%7D)
=
= 14.45 psia
Answer: r = 0.8081; s = -0.07071
Explanation:
A = (150i + 270j) mm
B = (300i - 450j) mm
C = (-100i - 250j) mm
R = rA + sB + C = 0i + 0j
R = r(150i + 270j) + s(300i - 450j) + (-100i - 250j) = 0i + 0j
R = (150r + 300s - 100)i + (270r - 450s - 250)j = 0i + 0j
Equating the i and j components;
150r + 300s - 100 = 0
270r - 450s - 250 = 0
150r + 300s = 100
270r - 450s = 250
solving simultaneously,
r = 0.8081 and s = -0.07071
QED!
The number of hectares of each crop he should plant are; 250 hectares of Corn, 500 hectares of Wheat and 450 hectares of soybeans
<h3>How to solve algebra word problem?</h3>
He grows corn, wheat and soya beans on the farm of 1200 hectares. Thus;
C + W + S = 12 ----(1)
It costs $45 per hectare to grow corn, $60 to grow wheat, and $50 to grow soybeans. Thus;
45C + 60W + 50S = 63750 -----(2)
He will grow twice as many hectares of wheat as corn. Thus;
W = 2C ------(3)
Put 2C for W in eq 1 and eq 2 to get;
C + 2C + S = 1200
3C + S = 1200 -----(4)
45C + 60(2C) + 50S = 63750
45C + 120C + 50S = 63750
165C + 50S = 63750 ------(5)
Solving eq 4 and 5 simultaneosly gives;
C = 250 and W = 500
Thus; S = 1200 - 3(250)
S = 450
Read more about algebra word problems at; brainly.com/question/13818690
I think the answer is B. 10D