Answer:
Explanation:
Mean temperature is given by
![T_mean = \frac{T_i + T_ \infinity}{2}\\\\T_mean = \frac{200 + 15}{2}](https://tex.z-dn.net/?f=T_mean%20%3D%20%5Cfrac%7BT_i%20%2B%20T_%20%5Cinfinity%7D%7B2%7D%5C%5C%5C%5CT_mean%20%3D%20%5Cfrac%7B200%20%2B%2015%7D%7B2%7D)
Tmean = (Ti + T∞)/2
![T_mean = 107.5^{0}](https://tex.z-dn.net/?f=T_mean%20%3D%20107.5%5E%7B0%7D)
Tmean = 107.5⁰C
Tmean = 107.5 + 273 = 380.5K
Properties of air at mean temperature
v = 24.2689 × 10⁻⁶m²/s
α = 35.024 × 10⁻⁶m²/s
= 221.6 × 10⁻⁷N.s/m²
= 0.0323 W/m.K
Cp = 1012 J/kg.K
Pr = v/α = 24.2689 × 10⁻⁶/35.024 × 10⁻⁶
= 0.693
Reynold's number, Re
Pv = 4m/πD²
where Re = (Pv * D)/![\mu](https://tex.z-dn.net/?f=%5Cmu)
Substituting for Pv
Re = 4m/(πD
)
= (4 x 0.003)/( π × 6 ×10⁻³ × 221.6 × 10⁻⁷)
= 28728.3
Since Re > 2000, the flow is turbulent
For turbulent flows, Use
Dittus - Doeltr correlation with n = 0.03
Nu = 0.023Re⁰⁸Pr⁰³ = (h₁D)/k
(h₁ × 0.006)/0.0323 = 0.023(28728.3)⁰⁸(0.693)⁰³
(h₁ × 0.006)/0.0323 = 75.962
h₁ = (75.962 × 0.0323)/0.006
h₁ = 408.93 W/m².K
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:
(A) Maximum voltage will be equal to 333.194 volt
(B) Current will be leading by an angle 54.70
Explanation:
We have given maximum current in the circuit ![i_m=385mA=385\times 10^{-3}A=0.385A](https://tex.z-dn.net/?f=i_m%3D385mA%3D385%5Ctimes%2010%5E%7B-3%7DA%3D0.385A)
Inductance of the inductor ![L=400mH=400\times 10^{-3}h=0.4H](https://tex.z-dn.net/?f=L%3D400mH%3D400%5Ctimes%2010%5E%7B-3%7Dh%3D0.4H)
Capacitance ![C=4.43\mu F=4.43\times 10^{-3}F](https://tex.z-dn.net/?f=C%3D4.43%5Cmu%20F%3D4.43%5Ctimes%2010%5E%7B-3%7DF)
Frequency is given f = 44 Hz
Resistance R = 500 ohm
Inductive reactance will be ![x_l=\omega L=2\times 3.14\times 44\times 0.4=110.528ohm](https://tex.z-dn.net/?f=x_l%3D%5Comega%20L%3D2%5Ctimes%203.14%5Ctimes%2044%5Ctimes%200.4%3D110.528ohm)
Capacitive reactance will be equal to ![X_C=\frac{1}{\omega C}=\frac{1}{2\times 3.14\times 44\times 4.43\times 10^{-6}}=816.82ohm](https://tex.z-dn.net/?f=X_C%3D%5Cfrac%7B1%7D%7B%5Comega%20C%7D%3D%5Cfrac%7B1%7D%7B2%5Ctimes%203.14%5Ctimes%2044%5Ctimes%204.43%5Ctimes%2010%5E%7B-6%7D%7D%3D816.82ohm)
Impedance of the circuit will be ![Z=\sqrt{R^2+(X_C-X_L)^2}=\sqrt{500^2+(816.92-110.52)^2}=865.44ohm](https://tex.z-dn.net/?f=Z%3D%5Csqrt%7BR%5E2%2B%28X_C-X_L%29%5E2%7D%3D%5Csqrt%7B500%5E2%2B%28816.92-110.52%29%5E2%7D%3D865.44ohm)
So maximum voltage will be ![\Delta V_{max}=0.385\times 865.44=333.194volt](https://tex.z-dn.net/?f=%5CDelta%20V_%7Bmax%7D%3D0.385%5Ctimes%20865.44%3D333.194volt)
(B) Phase difference will be given as ![\Phi =tan^{-1}\frac{X_C-X_L}{R}=\frac{816.92-110.52}{500}=54.70](https://tex.z-dn.net/?f=%5CPhi%20%3Dtan%5E%7B-1%7D%5Cfrac%7BX_C-X_L%7D%7BR%7D%3D%5Cfrac%7B816.92-110.52%7D%7B500%7D%3D54.70)
So current will be leading by an angle 54.70
Lo siento, no sé qué estás diciendo.